diff --git a/src/websockets/client.py b/src/websockets/client.py
index 633b1960..cfb441fd 100644
--- a/src/websockets/client.py
+++ b/src/websockets/client.py
@@ -1,7 +1,7 @@
 from __future__ import annotations
 
 import warnings
-from typing import Any, Generator, List, Optional, Sequence
+from typing import Any, Generator, List, Sequence
 
 from .datastructures import Headers, MultipleValuesError
 from .exceptions import (
@@ -73,12 +73,12 @@ def __init__(
         self,
         wsuri: WebSocketURI,
         *,
-        origin: Optional[Origin] = None,
-        extensions: Optional[Sequence[ClientExtensionFactory]] = None,
-        subprotocols: Optional[Sequence[Subprotocol]] = None,
+        origin: Origin | None = None,
+        extensions: Sequence[ClientExtensionFactory] | None = None,
+        subprotocols: Sequence[Subprotocol] | None = None,
         state: State = CONNECTING,
-        max_size: Optional[int] = 2**20,
-        logger: Optional[LoggerLike] = None,
+        max_size: int | None = 2**20,
+        logger: LoggerLike | None = None,
     ):
         super().__init__(
             side=CLIENT,
@@ -261,7 +261,7 @@ def process_extensions(self, headers: Headers) -> List[Extension]:
 
         return accepted_extensions
 
-    def process_subprotocol(self, headers: Headers) -> Optional[Subprotocol]:
+    def process_subprotocol(self, headers: Headers) -> Subprotocol | None:
         """
         Handle the Sec-WebSocket-Protocol HTTP response header.
 
@@ -274,7 +274,7 @@ def process_subprotocol(self, headers: Headers) -> Optional[Subprotocol]:
            Subprotocol, if one was selected.
 
         """
-        subprotocol: Optional[Subprotocol] = None
+        subprotocol: Subprotocol | None = None
 
         subprotocols = headers.get_all("Sec-WebSocket-Protocol")
 
diff --git a/src/websockets/exceptions.py b/src/websockets/exceptions.py
index f7169e3b..adb66e26 100644
--- a/src/websockets/exceptions.py
+++ b/src/websockets/exceptions.py
@@ -31,7 +31,6 @@
 from __future__ import annotations
 
 import http
-from typing import Optional
 
 from . import datastructures, frames, http11
 from .typing import StatusLike
@@ -78,11 +77,11 @@ class ConnectionClosed(WebSocketException):
     Raised when trying to interact with a closed connection.
 
     Attributes:
-        rcvd (Optional[Close]): if a close frame was received, its code and
+        rcvd (Close | None): if a close frame was received, its code and
             reason are available in ``rcvd.code`` and ``rcvd.reason``.
-        sent (Optional[Close]): if a close frame was sent, its code and reason
+        sent (Close | None): if a close frame was sent, its code and reason
             are available in ``sent.code`` and ``sent.reason``.
-        rcvd_then_sent (Optional[bool]): if close frames were received and
+        rcvd_then_sent (bool | None): if close frames were received and
             sent, this attribute tells in which order this happened, from the
             perspective of this side of the connection.
 
@@ -90,9 +89,9 @@ class ConnectionClosed(WebSocketException):
 
     def __init__(
         self,
-        rcvd: Optional[frames.Close],
-        sent: Optional[frames.Close],
-        rcvd_then_sent: Optional[bool] = None,
+        rcvd: frames.Close | None,
+        sent: frames.Close | None,
+        rcvd_then_sent: bool | None = None,
     ) -> None:
         self.rcvd = rcvd
         self.sent = sent
@@ -181,7 +180,7 @@ class InvalidHeader(InvalidHandshake):
 
     """
 
-    def __init__(self, name: str, value: Optional[str] = None) -> None:
+    def __init__(self, name: str, value: str | None = None) -> None:
         self.name = name
         self.value = value
 
@@ -221,7 +220,7 @@ class InvalidOrigin(InvalidHeader):
 
     """
 
-    def __init__(self, origin: Optional[str]) -> None:
+    def __init__(self, origin: str | None) -> None:
         super().__init__("Origin", origin)
 
 
@@ -301,7 +300,7 @@ class InvalidParameterValue(NegotiationError):
 
     """
 
-    def __init__(self, name: str, value: Optional[str]) -> None:
+    def __init__(self, name: str, value: str | None) -> None:
         self.name = name
         self.value = value
 
diff --git a/src/websockets/extensions/base.py b/src/websockets/extensions/base.py
index 7446c990..5b5528a0 100644
--- a/src/websockets/extensions/base.py
+++ b/src/websockets/extensions/base.py
@@ -1,6 +1,6 @@
 from __future__ import annotations
 
-from typing import List, Optional, Sequence, Tuple
+from typing import List, Sequence, Tuple
 
 from .. import frames
 from ..typing import ExtensionName, ExtensionParameter
@@ -22,7 +22,7 @@ def decode(
         self,
         frame: frames.Frame,
         *,
-        max_size: Optional[int] = None,
+        max_size: int | None = None,
     ) -> frames.Frame:
         """
         Decode an incoming frame.
diff --git a/src/websockets/extensions/permessage_deflate.py b/src/websockets/extensions/permessage_deflate.py
index edccac3c..e95b1064 100644
--- a/src/websockets/extensions/permessage_deflate.py
+++ b/src/websockets/extensions/permessage_deflate.py
@@ -2,7 +2,7 @@
 
 import dataclasses
 import zlib
-from typing import Any, Dict, List, Optional, Sequence, Tuple, Union
+from typing import Any, Dict, List, Sequence, Tuple, Union
 
 from .. import exceptions, frames
 from ..typing import ExtensionName, ExtensionParameter
@@ -36,7 +36,7 @@ def __init__(
         local_no_context_takeover: bool,
         remote_max_window_bits: int,
         local_max_window_bits: int,
-        compress_settings: Optional[Dict[Any, Any]] = None,
+        compress_settings: Dict[Any, Any] | None = None,
     ) -> None:
         """
         Configure the Per-Message Deflate extension.
@@ -84,7 +84,7 @@ def decode(
         self,
         frame: frames.Frame,
         *,
-        max_size: Optional[int] = None,
+        max_size: int | None = None,
     ) -> frames.Frame:
         """
         Decode an incoming frame.
@@ -174,8 +174,8 @@ def encode(self, frame: frames.Frame) -> frames.Frame:
 def _build_parameters(
     server_no_context_takeover: bool,
     client_no_context_takeover: bool,
-    server_max_window_bits: Optional[int],
-    client_max_window_bits: Optional[Union[int, bool]],
+    server_max_window_bits: int | None,
+    client_max_window_bits: Union[int, bool] | None,
 ) -> List[ExtensionParameter]:
     """
     Build a list of ``(name, value)`` pairs for some compression parameters.
@@ -197,7 +197,7 @@ def _build_parameters(
 
 def _extract_parameters(
     params: Sequence[ExtensionParameter], *, is_server: bool
-) -> Tuple[bool, bool, Optional[int], Optional[Union[int, bool]]]:
+) -> Tuple[bool, bool, int | None, Union[int, bool] | None]:
     """
     Extract compression parameters from a list of ``(name, value)`` pairs.
 
@@ -207,8 +207,8 @@ def _extract_parameters(
     """
     server_no_context_takeover: bool = False
     client_no_context_takeover: bool = False
-    server_max_window_bits: Optional[int] = None
-    client_max_window_bits: Optional[Union[int, bool]] = None
+    server_max_window_bits: int | None = None
+    client_max_window_bits: Union[int, bool] | None = None
 
     for name, value in params:
         if name == "server_no_context_takeover":
@@ -286,9 +286,9 @@ def __init__(
         self,
         server_no_context_takeover: bool = False,
         client_no_context_takeover: bool = False,
-        server_max_window_bits: Optional[int] = None,
-        client_max_window_bits: Optional[Union[int, bool]] = True,
-        compress_settings: Optional[Dict[str, Any]] = None,
+        server_max_window_bits: int | None = None,
+        client_max_window_bits: Union[int, bool] | None = True,
+        compress_settings: Dict[str, Any] | None = None,
     ) -> None:
         """
         Configure the Per-Message Deflate extension factory.
@@ -433,7 +433,7 @@ def process_response_params(
 
 
 def enable_client_permessage_deflate(
-    extensions: Optional[Sequence[ClientExtensionFactory]],
+    extensions: Sequence[ClientExtensionFactory] | None,
 ) -> Sequence[ClientExtensionFactory]:
     """
     Enable Per-Message Deflate with default settings in client extensions.
@@ -489,9 +489,9 @@ def __init__(
         self,
         server_no_context_takeover: bool = False,
         client_no_context_takeover: bool = False,
-        server_max_window_bits: Optional[int] = None,
-        client_max_window_bits: Optional[int] = None,
-        compress_settings: Optional[Dict[str, Any]] = None,
+        server_max_window_bits: int | None = None,
+        client_max_window_bits: int | None = None,
+        compress_settings: Dict[str, Any] | None = None,
         require_client_max_window_bits: bool = False,
     ) -> None:
         """
@@ -635,7 +635,7 @@ def process_request_params(
 
 
 def enable_server_permessage_deflate(
-    extensions: Optional[Sequence[ServerExtensionFactory]],
+    extensions: Sequence[ServerExtensionFactory] | None,
 ) -> Sequence[ServerExtensionFactory]:
     """
     Enable Per-Message Deflate with default settings in server extensions.
diff --git a/src/websockets/frames.py b/src/websockets/frames.py
index 862eef3a..5a304d6a 100644
--- a/src/websockets/frames.py
+++ b/src/websockets/frames.py
@@ -5,7 +5,7 @@
 import io
 import secrets
 import struct
-from typing import Callable, Generator, Optional, Sequence, Tuple
+from typing import Callable, Generator, Sequence, Tuple
 
 from . import exceptions, extensions
 from .typing import Data
@@ -205,8 +205,8 @@ def parse(
         read_exact: Callable[[int], Generator[None, None, bytes]],
         *,
         mask: bool,
-        max_size: Optional[int] = None,
-        extensions: Optional[Sequence[extensions.Extension]] = None,
+        max_size: int | None = None,
+        extensions: Sequence[extensions.Extension] | None = None,
     ) -> Generator[None, None, Frame]:
         """
         Parse a WebSocket frame.
@@ -280,7 +280,7 @@ def serialize(
         self,
         *,
         mask: bool,
-        extensions: Optional[Sequence[extensions.Extension]] = None,
+        extensions: Sequence[extensions.Extension] | None = None,
     ) -> bytes:
         """
         Serialize a WebSocket frame.
diff --git a/src/websockets/headers.py b/src/websockets/headers.py
index 463df306..3b316e0b 100644
--- a/src/websockets/headers.py
+++ b/src/websockets/headers.py
@@ -4,7 +4,7 @@
 import binascii
 import ipaddress
 import re
-from typing import Callable, List, Optional, Sequence, Tuple, TypeVar, cast
+from typing import Callable, List, Sequence, Tuple, TypeVar, cast
 
 from . import exceptions
 from .typing import (
@@ -63,7 +63,7 @@ def build_host(host: str, port: int, secure: bool) -> str:
 # https://www.rfc-editor.org/rfc/rfc7230.html#appendix-B.
 
 
-def peek_ahead(header: str, pos: int) -> Optional[str]:
+def peek_ahead(header: str, pos: int) -> str | None:
     """
     Return the next character from ``header`` at the given position.
 
@@ -314,7 +314,7 @@ def parse_extension_item_param(
     name, pos = parse_token(header, pos, header_name)
     pos = parse_OWS(header, pos)
     # Extract parameter value, if there is one.
-    value: Optional[str] = None
+    value: str | None = None
     if peek_ahead(header, pos) == "=":
         pos = parse_OWS(header, pos + 1)
         if peek_ahead(header, pos) == '"':
diff --git a/src/websockets/http11.py b/src/websockets/http11.py
index 6fe775ee..a7e9ae68 100644
--- a/src/websockets/http11.py
+++ b/src/websockets/http11.py
@@ -3,7 +3,7 @@
 import dataclasses
 import re
 import warnings
-from typing import Callable, Generator, Optional
+from typing import Callable, Generator
 
 from . import datastructures, exceptions
 
@@ -62,10 +62,10 @@ class Request:
     headers: datastructures.Headers
     # body isn't useful is the context of this library.
 
-    _exception: Optional[Exception] = None
+    _exception: Exception | None = None
 
     @property
-    def exception(self) -> Optional[Exception]:  # pragma: no cover
+    def exception(self) -> Exception | None:  # pragma: no cover
         warnings.warn(
             "Request.exception is deprecated; "
             "use ServerProtocol.handshake_exc instead",
@@ -164,12 +164,12 @@ class Response:
     status_code: int
     reason_phrase: str
     headers: datastructures.Headers
-    body: Optional[bytes] = None
+    body: bytes | None = None
 
-    _exception: Optional[Exception] = None
+    _exception: Exception | None = None
 
     @property
-    def exception(self) -> Optional[Exception]:  # pragma: no cover
+    def exception(self) -> Exception | None:  # pragma: no cover
         warnings.warn(
             "Response.exception is deprecated; "
             "use ClientProtocol.handshake_exc instead",
@@ -245,7 +245,7 @@ def parse(
         if 100 <= status_code < 200 or status_code == 204 or status_code == 304:
             body = None
         else:
-            content_length: Optional[int]
+            content_length: int | None
             try:
                 # MultipleValuesError is sufficiently unlikely that we don't
                 # attempt to handle it. Instead we document that its parent
diff --git a/src/websockets/imports.py b/src/websockets/imports.py
index a6a59d4c..9c05234f 100644
--- a/src/websockets/imports.py
+++ b/src/websockets/imports.py
@@ -1,7 +1,7 @@
 from __future__ import annotations
 
 import warnings
-from typing import Any, Dict, Iterable, Optional
+from typing import Any, Dict, Iterable
 
 
 __all__ = ["lazy_import"]
@@ -30,8 +30,8 @@ def import_name(name: str, source: str, namespace: Dict[str, Any]) -> Any:
 
 def lazy_import(
     namespace: Dict[str, Any],
-    aliases: Optional[Dict[str, str]] = None,
-    deprecated_aliases: Optional[Dict[str, str]] = None,
+    aliases: Dict[str, str] | None = None,
+    deprecated_aliases: Dict[str, str] | None = None,
 ) -> None:
     """
     Provide lazy, module-level imports.
diff --git a/src/websockets/legacy/auth.py b/src/websockets/legacy/auth.py
index 8217afed..067f9c78 100644
--- a/src/websockets/legacy/auth.py
+++ b/src/websockets/legacy/auth.py
@@ -3,7 +3,7 @@
 import functools
 import hmac
 import http
-from typing import Any, Awaitable, Callable, Iterable, Optional, Tuple, Union, cast
+from typing import Any, Awaitable, Callable, Iterable, Tuple, Union, cast
 
 from ..datastructures import Headers
 from ..exceptions import InvalidHeader
@@ -39,14 +39,14 @@ class BasicAuthWebSocketServerProtocol(WebSocketServerProtocol):
     encoding of non-ASCII characters is undefined.
     """
 
-    username: Optional[str] = None
+    username: str | None = None
     """Username of the authenticated user."""
 
     def __init__(
         self,
         *args: Any,
-        realm: Optional[str] = None,
-        check_credentials: Optional[Callable[[str, str], Awaitable[bool]]] = None,
+        realm: str | None = None,
+        check_credentials: Callable[[str, str], Awaitable[bool]] | None = None,
         **kwargs: Any,
     ) -> None:
         if realm is not None:
@@ -79,7 +79,7 @@ async def process_request(
         self,
         path: str,
         request_headers: Headers,
-    ) -> Optional[HTTPResponse]:
+    ) -> HTTPResponse | None:
         """
         Check HTTP Basic Auth and return an HTTP 401 response if needed.
 
@@ -115,10 +115,10 @@ async def process_request(
 
 
 def basic_auth_protocol_factory(
-    realm: Optional[str] = None,
-    credentials: Optional[Union[Credentials, Iterable[Credentials]]] = None,
-    check_credentials: Optional[Callable[[str, str], Awaitable[bool]]] = None,
-    create_protocol: Optional[Callable[..., BasicAuthWebSocketServerProtocol]] = None,
+    realm: str | None = None,
+    credentials: Union[Credentials, Iterable[Credentials]] | None = None,
+    check_credentials: Callable[[str, str], Awaitable[bool]] | None = None,
+    create_protocol: Callable[..., BasicAuthWebSocketServerProtocol] | None = None,
 ) -> Callable[..., BasicAuthWebSocketServerProtocol]:
     """
     Protocol factory that enforces HTTP Basic Auth.
diff --git a/src/websockets/legacy/client.py b/src/websockets/legacy/client.py
index e5da8b13..f7464368 100644
--- a/src/websockets/legacy/client.py
+++ b/src/websockets/legacy/client.py
@@ -13,7 +13,6 @@
     Callable,
     Generator,
     List,
-    Optional,
     Sequence,
     Tuple,
     Type,
@@ -86,12 +85,12 @@ class WebSocketClientProtocol(WebSocketCommonProtocol):
     def __init__(
         self,
         *,
-        logger: Optional[LoggerLike] = None,
-        origin: Optional[Origin] = None,
-        extensions: Optional[Sequence[ClientExtensionFactory]] = None,
-        subprotocols: Optional[Sequence[Subprotocol]] = None,
-        extra_headers: Optional[HeadersLike] = None,
-        user_agent_header: Optional[str] = USER_AGENT,
+        logger: LoggerLike | None = None,
+        origin: Origin | None = None,
+        extensions: Sequence[ClientExtensionFactory] | None = None,
+        subprotocols: Sequence[Subprotocol] | None = None,
+        extra_headers: HeadersLike | None = None,
+        user_agent_header: str | None = USER_AGENT,
         **kwargs: Any,
     ) -> None:
         if logger is None:
@@ -152,7 +151,7 @@ async def read_http_response(self) -> Tuple[int, Headers]:
     @staticmethod
     def process_extensions(
         headers: Headers,
-        available_extensions: Optional[Sequence[ClientExtensionFactory]],
+        available_extensions: Sequence[ClientExtensionFactory] | None,
     ) -> List[Extension]:
         """
         Handle the Sec-WebSocket-Extensions HTTP response header.
@@ -224,8 +223,8 @@ def process_extensions(
 
     @staticmethod
     def process_subprotocol(
-        headers: Headers, available_subprotocols: Optional[Sequence[Subprotocol]]
-    ) -> Optional[Subprotocol]:
+        headers: Headers, available_subprotocols: Sequence[Subprotocol] | None
+    ) -> Subprotocol | None:
         """
         Handle the Sec-WebSocket-Protocol HTTP response header.
 
@@ -234,7 +233,7 @@ def process_subprotocol(
         Return the selected subprotocol.
 
         """
-        subprotocol: Optional[Subprotocol] = None
+        subprotocol: Subprotocol | None = None
 
         header_values = headers.get_all("Sec-WebSocket-Protocol")
 
@@ -260,10 +259,10 @@ def process_subprotocol(
     async def handshake(
         self,
         wsuri: WebSocketURI,
-        origin: Optional[Origin] = None,
-        available_extensions: Optional[Sequence[ClientExtensionFactory]] = None,
-        available_subprotocols: Optional[Sequence[Subprotocol]] = None,
-        extra_headers: Optional[HeadersLike] = None,
+        origin: Origin | None = None,
+        available_extensions: Sequence[ClientExtensionFactory] | None = None,
+        available_subprotocols: Sequence[Subprotocol] | None = None,
+        extra_headers: HeadersLike | None = None,
     ) -> None:
         """
         Perform the client side of the opening handshake.
@@ -427,26 +426,26 @@ def __init__(
         self,
         uri: str,
         *,
-        create_protocol: Optional[Callable[..., WebSocketClientProtocol]] = None,
-        logger: Optional[LoggerLike] = None,
-        compression: Optional[str] = "deflate",
-        origin: Optional[Origin] = None,
-        extensions: Optional[Sequence[ClientExtensionFactory]] = None,
-        subprotocols: Optional[Sequence[Subprotocol]] = None,
-        extra_headers: Optional[HeadersLike] = None,
-        user_agent_header: Optional[str] = USER_AGENT,
-        open_timeout: Optional[float] = 10,
-        ping_interval: Optional[float] = 20,
-        ping_timeout: Optional[float] = 20,
-        close_timeout: Optional[float] = None,
-        max_size: Optional[int] = 2**20,
-        max_queue: Optional[int] = 2**5,
+        create_protocol: Callable[..., WebSocketClientProtocol] | None = None,
+        logger: LoggerLike | None = None,
+        compression: str | None = "deflate",
+        origin: Origin | None = None,
+        extensions: Sequence[ClientExtensionFactory] | None = None,
+        subprotocols: Sequence[Subprotocol] | None = None,
+        extra_headers: HeadersLike | None = None,
+        user_agent_header: str | None = USER_AGENT,
+        open_timeout: float | None = 10,
+        ping_interval: float | None = 20,
+        ping_timeout: float | None = 20,
+        close_timeout: float | None = None,
+        max_size: int | None = 2**20,
+        max_queue: int | None = 2**5,
         read_limit: int = 2**16,
         write_limit: int = 2**16,
         **kwargs: Any,
     ) -> None:
         # Backwards compatibility: close_timeout used to be called timeout.
-        timeout: Optional[float] = kwargs.pop("timeout", None)
+        timeout: float | None = kwargs.pop("timeout", None)
         if timeout is None:
             timeout = 10
         else:
@@ -456,7 +455,7 @@ def __init__(
             close_timeout = timeout
 
         # Backwards compatibility: create_protocol used to be called klass.
-        klass: Optional[Type[WebSocketClientProtocol]] = kwargs.pop("klass", None)
+        klass: Type[WebSocketClientProtocol] | None = kwargs.pop("klass", None)
         if klass is None:
             klass = WebSocketClientProtocol
         else:
@@ -469,7 +468,7 @@ def __init__(
         legacy_recv: bool = kwargs.pop("legacy_recv", False)
 
         # Backwards compatibility: the loop parameter used to be supported.
-        _loop: Optional[asyncio.AbstractEventLoop] = kwargs.pop("loop", None)
+        _loop: asyncio.AbstractEventLoop | None = kwargs.pop("loop", None)
         if _loop is None:
             loop = asyncio.get_event_loop()
         else:
@@ -516,13 +515,13 @@ def __init__(
         )
 
         if kwargs.pop("unix", False):
-            path: Optional[str] = kwargs.pop("path", None)
+            path: str | None = kwargs.pop("path", None)
             create_connection = functools.partial(
                 loop.create_unix_connection, factory, path, **kwargs
             )
         else:
-            host: Optional[str]
-            port: Optional[int]
+            host: str | None
+            port: int | None
             if kwargs.get("sock") is None:
                 host, port = wsuri.host, wsuri.port
             else:
@@ -630,9 +629,9 @@ async def __aenter__(self) -> WebSocketClientProtocol:
 
     async def __aexit__(
         self,
-        exc_type: Optional[Type[BaseException]],
-        exc_value: Optional[BaseException],
-        traceback: Optional[TracebackType],
+        exc_type: Type[BaseException] | None,
+        exc_value: BaseException | None,
+        traceback: TracebackType | None,
     ) -> None:
         await self.protocol.close()
 
@@ -679,7 +678,7 @@ async def __await_impl__(self) -> WebSocketClientProtocol:
 
 
 def unix_connect(
-    path: Optional[str] = None,
+    path: str | None = None,
     uri: str = "ws://localhost/",
     **kwargs: Any,
 ) -> Connect:
diff --git a/src/websockets/legacy/framing.py b/src/websockets/legacy/framing.py
index b77b869e..8a13fa44 100644
--- a/src/websockets/legacy/framing.py
+++ b/src/websockets/legacy/framing.py
@@ -1,7 +1,7 @@
 from __future__ import annotations
 
 import struct
-from typing import Any, Awaitable, Callable, NamedTuple, Optional, Sequence, Tuple
+from typing import Any, Awaitable, Callable, NamedTuple, Sequence, Tuple
 
 from .. import extensions, frames
 from ..exceptions import PayloadTooBig, ProtocolError
@@ -44,8 +44,8 @@ async def read(
         reader: Callable[[int], Awaitable[bytes]],
         *,
         mask: bool,
-        max_size: Optional[int] = None,
-        extensions: Optional[Sequence[extensions.Extension]] = None,
+        max_size: int | None = None,
+        extensions: Sequence[extensions.Extension] | None = None,
     ) -> Frame:
         """
         Read a WebSocket frame.
@@ -122,7 +122,7 @@ def write(
         write: Callable[[bytes], Any],
         *,
         mask: bool,
-        extensions: Optional[Sequence[extensions.Extension]] = None,
+        extensions: Sequence[extensions.Extension] | None = None,
     ) -> None:
         """
         Write a WebSocket frame.
diff --git a/src/websockets/legacy/protocol.py b/src/websockets/legacy/protocol.py
index 26d50a2c..94d42cfd 100644
--- a/src/websockets/legacy/protocol.py
+++ b/src/websockets/legacy/protocol.py
@@ -22,7 +22,6 @@
     Iterable,
     List,
     Mapping,
-    Optional,
     Tuple,
     Union,
     cast,
@@ -173,21 +172,21 @@ class WebSocketCommonProtocol(asyncio.Protocol):
     def __init__(
         self,
         *,
-        logger: Optional[LoggerLike] = None,
-        ping_interval: Optional[float] = 20,
-        ping_timeout: Optional[float] = 20,
-        close_timeout: Optional[float] = None,
-        max_size: Optional[int] = 2**20,
-        max_queue: Optional[int] = 2**5,
+        logger: LoggerLike | None = None,
+        ping_interval: float | None = 20,
+        ping_timeout: float | None = 20,
+        close_timeout: float | None = None,
+        max_size: int | None = 2**20,
+        max_queue: int | None = 2**5,
         read_limit: int = 2**16,
         write_limit: int = 2**16,
         # The following arguments are kept only for backwards compatibility.
-        host: Optional[str] = None,
-        port: Optional[int] = None,
-        secure: Optional[bool] = None,
+        host: str | None = None,
+        port: int | None = None,
+        secure: bool | None = None,
         legacy_recv: bool = False,
-        loop: Optional[asyncio.AbstractEventLoop] = None,
-        timeout: Optional[float] = None,
+        loop: asyncio.AbstractEventLoop | None = None,
+        timeout: float | None = None,
     ) -> None:
         if legacy_recv:  # pragma: no cover
             warnings.warn("legacy_recv is deprecated", DeprecationWarning)
@@ -243,7 +242,7 @@ def __init__(
 
         # Copied from asyncio.FlowControlMixin
         self._paused = False
-        self._drain_waiter: Optional[asyncio.Future[None]] = None
+        self._drain_waiter: asyncio.Future[None] | None = None
 
         self._drain_lock = asyncio.Lock()
 
@@ -265,13 +264,13 @@ def __init__(
 
         # WebSocket protocol parameters.
         self.extensions: List[Extension] = []
-        self.subprotocol: Optional[Subprotocol] = None
+        self.subprotocol: Subprotocol | None = None
         """Subprotocol, if one was negotiated."""
 
         # Close code and reason, set when a close frame is sent or received.
-        self.close_rcvd: Optional[Close] = None
-        self.close_sent: Optional[Close] = None
-        self.close_rcvd_then_sent: Optional[bool] = None
+        self.close_rcvd: Close | None = None
+        self.close_sent: Close | None = None
+        self.close_rcvd_then_sent: bool | None = None
 
         # Completed when the connection state becomes CLOSED. Translates the
         # :meth:`connection_lost` callback to a :class:`~asyncio.Future`
@@ -281,11 +280,11 @@ def __init__(
 
         # Queue of received messages.
         self.messages: Deque[Data] = collections.deque()
-        self._pop_message_waiter: Optional[asyncio.Future[None]] = None
-        self._put_message_waiter: Optional[asyncio.Future[None]] = None
+        self._pop_message_waiter: asyncio.Future[None] | None = None
+        self._put_message_waiter: asyncio.Future[None] | None = None
 
         # Protect sending fragmented messages.
-        self._fragmented_message_waiter: Optional[asyncio.Future[None]] = None
+        self._fragmented_message_waiter: asyncio.Future[None] | None = None
 
         # Mapping of ping IDs to pong waiters, in chronological order.
         self.pings: Dict[bytes, Tuple[asyncio.Future[float], float]] = {}
@@ -306,7 +305,7 @@ def __init__(
         self.transfer_data_task: asyncio.Task[None]
 
         # Exception that occurred during data transfer, if any.
-        self.transfer_data_exc: Optional[BaseException] = None
+        self.transfer_data_exc: BaseException | None = None
 
         # Task sending keepalive pings.
         self.keepalive_ping_task: asyncio.Task[None]
@@ -363,19 +362,19 @@ def connection_open(self) -> None:
         self.close_connection_task = self.loop.create_task(self.close_connection())
 
     @property
-    def host(self) -> Optional[str]:
+    def host(self) -> str | None:
         alternative = "remote_address" if self.is_client else "local_address"
         warnings.warn(f"use {alternative}[0] instead of host", DeprecationWarning)
         return self._host
 
     @property
-    def port(self) -> Optional[int]:
+    def port(self) -> int | None:
         alternative = "remote_address" if self.is_client else "local_address"
         warnings.warn(f"use {alternative}[1] instead of port", DeprecationWarning)
         return self._port
 
     @property
-    def secure(self) -> Optional[bool]:
+    def secure(self) -> bool | None:
         warnings.warn("don't use secure", DeprecationWarning)
         return self._secure
 
@@ -447,7 +446,7 @@ def closed(self) -> bool:
         return self.state is State.CLOSED
 
     @property
-    def close_code(self) -> Optional[int]:
+    def close_code(self) -> int | None:
         """
         WebSocket close code, defined in `section 7.1.5 of RFC 6455`_.
 
@@ -465,7 +464,7 @@ def close_code(self) -> Optional[int]:
             return self.close_rcvd.code
 
     @property
-    def close_reason(self) -> Optional[str]:
+    def close_reason(self) -> str | None:
         """
         WebSocket close reason, defined in `section 7.1.6 of RFC 6455`_.
 
@@ -804,7 +803,7 @@ async def wait_closed(self) -> None:
         """
         await asyncio.shield(self.connection_lost_waiter)
 
-    async def ping(self, data: Optional[Data] = None) -> Awaitable[float]:
+    async def ping(self, data: Data | None = None) -> Awaitable[float]:
         """
         Send a Ping_.
 
@@ -1017,7 +1016,7 @@ async def transfer_data(self) -> None:
             self.transfer_data_exc = exc
             self.fail_connection(CloseCode.INTERNAL_ERROR)
 
-    async def read_message(self) -> Optional[Data]:
+    async def read_message(self) -> Data | None:
         """
         Read a single message from the connection.
 
@@ -1090,7 +1089,7 @@ def append(frame: Frame) -> None:
 
         return ("" if text else b"").join(fragments)
 
-    async def read_data_frame(self, max_size: Optional[int]) -> Optional[Frame]:
+    async def read_data_frame(self, max_size: int | None) -> Frame | None:
         """
         Read a single data frame from the connection.
 
@@ -1153,7 +1152,7 @@ async def read_data_frame(self, max_size: Optional[int]) -> Optional[Frame]:
             else:
                 return frame
 
-    async def read_frame(self, max_size: Optional[int]) -> Frame:
+    async def read_frame(self, max_size: int | None) -> Frame:
         """
         Read a single frame from the connection.
 
@@ -1204,9 +1203,7 @@ async def write_frame(
         self.write_frame_sync(fin, opcode, data)
         await self.drain()
 
-    async def write_close_frame(
-        self, close: Close, data: Optional[bytes] = None
-    ) -> None:
+    async def write_close_frame(self, close: Close, data: bytes | None = None) -> None:
         """
         Write a close frame if and only if the connection state is OPEN.
 
@@ -1484,7 +1481,7 @@ def connection_made(self, transport: asyncio.BaseTransport) -> None:
         # Copied from asyncio.StreamReaderProtocol
         self.reader.set_transport(transport)
 
-    def connection_lost(self, exc: Optional[Exception]) -> None:
+    def connection_lost(self, exc: Exception | None) -> None:
         """
         7.1.4. The WebSocket Connection is Closed.
 
diff --git a/src/websockets/legacy/server.py b/src/websockets/legacy/server.py
index 0f3c1c15..55111517 100644
--- a/src/websockets/legacy/server.py
+++ b/src/websockets/legacy/server.py
@@ -16,7 +16,6 @@
     Generator,
     Iterable,
     List,
-    Optional,
     Sequence,
     Set,
     Tuple,
@@ -103,19 +102,19 @@ def __init__(
         ],
         ws_server: WebSocketServer,
         *,
-        logger: Optional[LoggerLike] = None,
-        origins: Optional[Sequence[Optional[Origin]]] = None,
-        extensions: Optional[Sequence[ServerExtensionFactory]] = None,
-        subprotocols: Optional[Sequence[Subprotocol]] = None,
-        extra_headers: Optional[HeadersLikeOrCallable] = None,
-        server_header: Optional[str] = USER_AGENT,
-        process_request: Optional[
-            Callable[[str, Headers], Awaitable[Optional[HTTPResponse]]]
-        ] = None,
-        select_subprotocol: Optional[
-            Callable[[Sequence[Subprotocol], Sequence[Subprotocol]], Subprotocol]
-        ] = None,
-        open_timeout: Optional[float] = 10,
+        logger: LoggerLike | None = None,
+        origins: Sequence[Origin | None] | None = None,
+        extensions: Sequence[ServerExtensionFactory] | None = None,
+        subprotocols: Sequence[Subprotocol] | None = None,
+        extra_headers: HeadersLikeOrCallable | None = None,
+        server_header: str | None = USER_AGENT,
+        process_request: (
+            Callable[[str, Headers], Awaitable[HTTPResponse | None]] | None
+        ) = None,
+        select_subprotocol: (
+            Callable[[Sequence[Subprotocol], Sequence[Subprotocol]], Subprotocol] | None
+        ) = None,
+        open_timeout: float | None = 10,
         **kwargs: Any,
     ) -> None:
         if logger is None:
@@ -293,7 +292,7 @@ async def read_http_request(self) -> Tuple[str, Headers]:
         return path, headers
 
     def write_http_response(
-        self, status: http.HTTPStatus, headers: Headers, body: Optional[bytes] = None
+        self, status: http.HTTPStatus, headers: Headers, body: bytes | None = None
     ) -> None:
         """
         Write status line and headers to the HTTP response.
@@ -322,7 +321,7 @@ def write_http_response(
 
     async def process_request(
         self, path: str, request_headers: Headers
-    ) -> Optional[HTTPResponse]:
+    ) -> HTTPResponse | None:
         """
         Intercept the HTTP request and return an HTTP response if appropriate.
 
@@ -371,8 +370,8 @@ async def process_request(
 
     @staticmethod
     def process_origin(
-        headers: Headers, origins: Optional[Sequence[Optional[Origin]]] = None
-    ) -> Optional[Origin]:
+        headers: Headers, origins: Sequence[Origin | None] | None = None
+    ) -> Origin | None:
         """
         Handle the Origin HTTP request header.
 
@@ -387,9 +386,11 @@ def process_origin(
         # "The user agent MUST NOT include more than one Origin header field"
         # per https://www.rfc-editor.org/rfc/rfc6454.html#section-7.3.
         try:
-            origin = cast(Optional[Origin], headers.get("Origin"))
+            origin = headers.get("Origin")
         except MultipleValuesError as exc:
             raise InvalidHeader("Origin", "more than one Origin header found") from exc
+        if origin is not None:
+            origin = cast(Origin, origin)
         if origins is not None:
             if origin not in origins:
                 raise InvalidOrigin(origin)
@@ -398,8 +399,8 @@ def process_origin(
     @staticmethod
     def process_extensions(
         headers: Headers,
-        available_extensions: Optional[Sequence[ServerExtensionFactory]],
-    ) -> Tuple[Optional[str], List[Extension]]:
+        available_extensions: Sequence[ServerExtensionFactory] | None,
+    ) -> Tuple[str | None, List[Extension]]:
         """
         Handle the Sec-WebSocket-Extensions HTTP request header.
 
@@ -435,7 +436,7 @@ def process_extensions(
             InvalidHandshake: To abort the handshake with an HTTP 400 error.
 
         """
-        response_header_value: Optional[str] = None
+        response_header_value: str | None = None
 
         extension_headers: List[ExtensionHeader] = []
         accepted_extensions: List[Extension] = []
@@ -479,8 +480,8 @@ def process_extensions(
 
     # Not @staticmethod because it calls self.select_subprotocol()
     def process_subprotocol(
-        self, headers: Headers, available_subprotocols: Optional[Sequence[Subprotocol]]
-    ) -> Optional[Subprotocol]:
+        self, headers: Headers, available_subprotocols: Sequence[Subprotocol] | None
+    ) -> Subprotocol | None:
         """
         Handle the Sec-WebSocket-Protocol HTTP request header.
 
@@ -495,7 +496,7 @@ def process_subprotocol(
             InvalidHandshake: To abort the handshake with an HTTP 400 error.
 
         """
-        subprotocol: Optional[Subprotocol] = None
+        subprotocol: Subprotocol | None = None
 
         header_values = headers.get_all("Sec-WebSocket-Protocol")
 
@@ -514,7 +515,7 @@ def select_subprotocol(
         self,
         client_subprotocols: Sequence[Subprotocol],
         server_subprotocols: Sequence[Subprotocol],
-    ) -> Optional[Subprotocol]:
+    ) -> Subprotocol | None:
         """
         Pick a subprotocol among those supported by the client and the server.
 
@@ -552,10 +553,10 @@ def select_subprotocol(
 
     async def handshake(
         self,
-        origins: Optional[Sequence[Optional[Origin]]] = None,
-        available_extensions: Optional[Sequence[ServerExtensionFactory]] = None,
-        available_subprotocols: Optional[Sequence[Subprotocol]] = None,
-        extra_headers: Optional[HeadersLikeOrCallable] = None,
+        origins: Sequence[Origin | None] | None = None,
+        available_extensions: Sequence[ServerExtensionFactory] | None = None,
+        available_subprotocols: Sequence[Subprotocol] | None = None,
+        extra_headers: HeadersLikeOrCallable | None = None,
     ) -> str:
         """
         Perform the server side of the opening handshake.
@@ -661,7 +662,7 @@ class WebSocketServer:
 
     """
 
-    def __init__(self, logger: Optional[LoggerLike] = None):
+    def __init__(self, logger: LoggerLike | None = None):
         if logger is None:
             logger = logging.getLogger("websockets.server")
         self.logger = logger
@@ -670,7 +671,7 @@ def __init__(self, logger: Optional[LoggerLike] = None):
         self.websockets: Set[WebSocketServerProtocol] = set()
 
         # Task responsible for closing the server and terminating connections.
-        self.close_task: Optional[asyncio.Task[None]] = None
+        self.close_task: asyncio.Task[None] | None = None
 
         # Completed when the server is closed and connections are terminated.
         self.closed_waiter: asyncio.Future[None]
@@ -869,9 +870,9 @@ async def __aenter__(self) -> WebSocketServer:  # pragma: no cover
 
     async def __aexit__(
         self,
-        exc_type: Optional[Type[BaseException]],
-        exc_value: Optional[BaseException],
-        traceback: Optional[TracebackType],
+        exc_type: Type[BaseException] | None,
+        exc_value: BaseException | None,
+        traceback: TracebackType | None,
     ) -> None:  # pragma: no cover
         self.close()
         await self.wait_closed()
@@ -941,8 +942,8 @@ class Serve:
         server_header: Value of  the ``Server`` response header.
             It defaults to ``"Python/x.y.z websockets/X.Y"``.
             Setting it to :obj:`None` removes the header.
-        process_request (Optional[Callable[[str, Headers], \
-            Awaitable[Optional[Tuple[StatusLike, HeadersLike, bytes]]]]]):
+        process_request (Callable[[str, Headers], \
+            Awaitable[Tuple[StatusLike, HeadersLike, bytes] | None]] | None):
             Intercept HTTP request before the opening handshake.
             See :meth:`~WebSocketServerProtocol.process_request` for details.
         select_subprotocol: Select a subprotocol supported by the client.
@@ -975,35 +976,35 @@ def __init__(
             Callable[[WebSocketServerProtocol], Awaitable[Any]],
             Callable[[WebSocketServerProtocol, str], Awaitable[Any]],  # deprecated
         ],
-        host: Optional[Union[str, Sequence[str]]] = None,
-        port: Optional[int] = None,
+        host: Union[str, Sequence[str]] | None = None,
+        port: int | None = None,
         *,
-        create_protocol: Optional[Callable[..., WebSocketServerProtocol]] = None,
-        logger: Optional[LoggerLike] = None,
-        compression: Optional[str] = "deflate",
-        origins: Optional[Sequence[Optional[Origin]]] = None,
-        extensions: Optional[Sequence[ServerExtensionFactory]] = None,
-        subprotocols: Optional[Sequence[Subprotocol]] = None,
-        extra_headers: Optional[HeadersLikeOrCallable] = None,
-        server_header: Optional[str] = USER_AGENT,
-        process_request: Optional[
-            Callable[[str, Headers], Awaitable[Optional[HTTPResponse]]]
-        ] = None,
-        select_subprotocol: Optional[
-            Callable[[Sequence[Subprotocol], Sequence[Subprotocol]], Subprotocol]
-        ] = None,
-        open_timeout: Optional[float] = 10,
-        ping_interval: Optional[float] = 20,
-        ping_timeout: Optional[float] = 20,
-        close_timeout: Optional[float] = None,
-        max_size: Optional[int] = 2**20,
-        max_queue: Optional[int] = 2**5,
+        create_protocol: Callable[..., WebSocketServerProtocol] | None = None,
+        logger: LoggerLike | None = None,
+        compression: str | None = "deflate",
+        origins: Sequence[Origin | None] | None = None,
+        extensions: Sequence[ServerExtensionFactory] | None = None,
+        subprotocols: Sequence[Subprotocol] | None = None,
+        extra_headers: HeadersLikeOrCallable | None = None,
+        server_header: str | None = USER_AGENT,
+        process_request: (
+            Callable[[str, Headers], Awaitable[HTTPResponse | None]] | None
+        ) = None,
+        select_subprotocol: (
+            Callable[[Sequence[Subprotocol], Sequence[Subprotocol]], Subprotocol] | None
+        ) = None,
+        open_timeout: float | None = 10,
+        ping_interval: float | None = 20,
+        ping_timeout: float | None = 20,
+        close_timeout: float | None = None,
+        max_size: int | None = 2**20,
+        max_queue: int | None = 2**5,
         read_limit: int = 2**16,
         write_limit: int = 2**16,
         **kwargs: Any,
     ) -> None:
         # Backwards compatibility: close_timeout used to be called timeout.
-        timeout: Optional[float] = kwargs.pop("timeout", None)
+        timeout: float | None = kwargs.pop("timeout", None)
         if timeout is None:
             timeout = 10
         else:
@@ -1013,7 +1014,7 @@ def __init__(
             close_timeout = timeout
 
         # Backwards compatibility: create_protocol used to be called klass.
-        klass: Optional[Type[WebSocketServerProtocol]] = kwargs.pop("klass", None)
+        klass: Type[WebSocketServerProtocol] | None = kwargs.pop("klass", None)
         if klass is None:
             klass = WebSocketServerProtocol
         else:
@@ -1026,7 +1027,7 @@ def __init__(
         legacy_recv: bool = kwargs.pop("legacy_recv", False)
 
         # Backwards compatibility: the loop parameter used to be supported.
-        _loop: Optional[asyncio.AbstractEventLoop] = kwargs.pop("loop", None)
+        _loop: asyncio.AbstractEventLoop | None = kwargs.pop("loop", None)
         if _loop is None:
             loop = asyncio.get_event_loop()
         else:
@@ -1076,7 +1077,7 @@ def __init__(
         )
 
         if kwargs.pop("unix", False):
-            path: Optional[str] = kwargs.pop("path", None)
+            path: str | None = kwargs.pop("path", None)
             # unix_serve(path) must not specify host and port parameters.
             assert host is None and port is None
             create_server = functools.partial(
@@ -1098,9 +1099,9 @@ async def __aenter__(self) -> WebSocketServer:
 
     async def __aexit__(
         self,
-        exc_type: Optional[Type[BaseException]],
-        exc_value: Optional[BaseException],
-        traceback: Optional[TracebackType],
+        exc_type: Type[BaseException] | None,
+        exc_value: BaseException | None,
+        traceback: TracebackType | None,
     ) -> None:
         self.ws_server.close()
         await self.ws_server.wait_closed()
@@ -1129,7 +1130,7 @@ def unix_serve(
         Callable[[WebSocketServerProtocol], Awaitable[Any]],
         Callable[[WebSocketServerProtocol, str], Awaitable[Any]],  # deprecated
     ],
-    path: Optional[str] = None,
+    path: str | None = None,
     **kwargs: Any,
 ) -> Serve:
     """
diff --git a/src/websockets/protocol.py b/src/websockets/protocol.py
index 0b36202e..8aa222ee 100644
--- a/src/websockets/protocol.py
+++ b/src/websockets/protocol.py
@@ -3,7 +3,7 @@
 import enum
 import logging
 import uuid
-from typing import Generator, List, Optional, Type, Union
+from typing import Generator, List, Type, Union
 
 from .exceptions import (
     ConnectionClosed,
@@ -89,8 +89,8 @@ def __init__(
         side: Side,
         *,
         state: State = OPEN,
-        max_size: Optional[int] = 2**20,
-        logger: Optional[LoggerLike] = None,
+        max_size: int | None = 2**20,
+        logger: LoggerLike | None = None,
     ) -> None:
         # Unique identifier. For logs.
         self.id: uuid.UUID = uuid.uuid4()
@@ -116,24 +116,24 @@ def __init__(
 
         # Current size of incoming message in bytes. Only set while reading a
         # fragmented message i.e. a data frames with the FIN bit not set.
-        self.cur_size: Optional[int] = None
+        self.cur_size: int | None = None
 
         # True while sending a fragmented message i.e. a data frames with the
         # FIN bit not set.
         self.expect_continuation_frame = False
 
         # WebSocket protocol parameters.
-        self.origin: Optional[Origin] = None
+        self.origin: Origin | None = None
         self.extensions: List[Extension] = []
-        self.subprotocol: Optional[Subprotocol] = None
+        self.subprotocol: Subprotocol | None = None
 
         # Close code and reason, set when a close frame is sent or received.
-        self.close_rcvd: Optional[Close] = None
-        self.close_sent: Optional[Close] = None
-        self.close_rcvd_then_sent: Optional[bool] = None
+        self.close_rcvd: Close | None = None
+        self.close_sent: Close | None = None
+        self.close_rcvd_then_sent: bool | None = None
 
         # Track if an exception happened during the handshake.
-        self.handshake_exc: Optional[Exception] = None
+        self.handshake_exc: Exception | None = None
         """
         Exception to raise if the opening handshake failed.
 
@@ -150,7 +150,7 @@ def __init__(
         self.writes: List[bytes] = []
         self.parser = self.parse()
         next(self.parser)  # start coroutine
-        self.parser_exc: Optional[Exception] = None
+        self.parser_exc: Exception | None = None
 
     @property
     def state(self) -> State:
@@ -169,7 +169,7 @@ def state(self, state: State) -> None:
         self._state = state
 
     @property
-    def close_code(self) -> Optional[int]:
+    def close_code(self) -> int | None:
         """
         `WebSocket close code`_.
 
@@ -187,7 +187,7 @@ def close_code(self) -> Optional[int]:
             return self.close_rcvd.code
 
     @property
-    def close_reason(self) -> Optional[str]:
+    def close_reason(self) -> str | None:
         """
         `WebSocket close reason`_.
 
@@ -348,7 +348,7 @@ def send_binary(self, data: bytes, fin: bool = True) -> None:
         self.expect_continuation_frame = not fin
         self.send_frame(Frame(OP_BINARY, data, fin))
 
-    def send_close(self, code: Optional[int] = None, reason: str = "") -> None:
+    def send_close(self, code: int | None = None, reason: str = "") -> None:
         """
         Send a `Close frame`_.
 
diff --git a/src/websockets/server.py b/src/websockets/server.py
index 330e54f3..a9254108 100644
--- a/src/websockets/server.py
+++ b/src/websockets/server.py
@@ -5,7 +5,7 @@
 import email.utils
 import http
 import warnings
-from typing import Any, Callable, Generator, List, Optional, Sequence, Tuple, cast
+from typing import Any, Callable, Generator, List, Sequence, Tuple, cast
 
 from .datastructures import Headers, MultipleValuesError
 from .exceptions import (
@@ -77,18 +77,19 @@ class ServerProtocol(Protocol):
     def __init__(
         self,
         *,
-        origins: Optional[Sequence[Optional[Origin]]] = None,
-        extensions: Optional[Sequence[ServerExtensionFactory]] = None,
-        subprotocols: Optional[Sequence[Subprotocol]] = None,
-        select_subprotocol: Optional[
+        origins: Sequence[Origin | None] | None = None,
+        extensions: Sequence[ServerExtensionFactory] | None = None,
+        subprotocols: Sequence[Subprotocol] | None = None,
+        select_subprotocol: (
             Callable[
                 [ServerProtocol, Sequence[Subprotocol]],
-                Optional[Subprotocol],
+                Subprotocol | None,
             ]
-        ] = None,
+            | None
+        ) = None,
         state: State = CONNECTING,
-        max_size: Optional[int] = 2**20,
-        logger: Optional[LoggerLike] = None,
+        max_size: int | None = 2**20,
+        logger: LoggerLike | None = None,
     ):
         super().__init__(
             side=SERVER,
@@ -200,7 +201,7 @@ def accept(self, request: Request) -> Response:
     def process_request(
         self,
         request: Request,
-    ) -> Tuple[str, Optional[str], Optional[str]]:
+    ) -> Tuple[str, str | None, str | None]:
         """
         Check a handshake request and negotiate extensions and subprotocol.
 
@@ -285,7 +286,7 @@ def process_request(
             protocol_header,
         )
 
-    def process_origin(self, headers: Headers) -> Optional[Origin]:
+    def process_origin(self, headers: Headers) -> Origin | None:
         """
         Handle the Origin HTTP request header.
 
@@ -303,9 +304,11 @@ def process_origin(self, headers: Headers) -> Optional[Origin]:
         # "The user agent MUST NOT include more than one Origin header field"
         # per https://www.rfc-editor.org/rfc/rfc6454.html#section-7.3.
         try:
-            origin = cast(Optional[Origin], headers.get("Origin"))
+            origin = headers.get("Origin")
         except MultipleValuesError as exc:
             raise InvalidHeader("Origin", "more than one Origin header found") from exc
+        if origin is not None:
+            origin = cast(Origin, origin)
         if self.origins is not None:
             if origin not in self.origins:
                 raise InvalidOrigin(origin)
@@ -314,7 +317,7 @@ def process_origin(self, headers: Headers) -> Optional[Origin]:
     def process_extensions(
         self,
         headers: Headers,
-    ) -> Tuple[Optional[str], List[Extension]]:
+    ) -> Tuple[str | None, List[Extension]]:
         """
         Handle the Sec-WebSocket-Extensions HTTP request header.
 
@@ -350,7 +353,7 @@ def process_extensions(
             InvalidHandshake: If the Sec-WebSocket-Extensions header is invalid.
 
         """
-        response_header_value: Optional[str] = None
+        response_header_value: str | None = None
 
         extension_headers: List[ExtensionHeader] = []
         accepted_extensions: List[Extension] = []
@@ -392,7 +395,7 @@ def process_extensions(
 
         return response_header_value, accepted_extensions
 
-    def process_subprotocol(self, headers: Headers) -> Optional[Subprotocol]:
+    def process_subprotocol(self, headers: Headers) -> Subprotocol | None:
         """
         Handle the Sec-WebSocket-Protocol HTTP request header.
 
@@ -420,7 +423,7 @@ def process_subprotocol(self, headers: Headers) -> Optional[Subprotocol]:
     def select_subprotocol(
         self,
         subprotocols: Sequence[Subprotocol],
-    ) -> Optional[Subprotocol]:
+    ) -> Subprotocol | None:
         """
         Pick a subprotocol among those offered by the client.
 
diff --git a/src/websockets/sync/client.py b/src/websockets/sync/client.py
index 0bb7a76f..60b49ebc 100644
--- a/src/websockets/sync/client.py
+++ b/src/websockets/sync/client.py
@@ -4,7 +4,7 @@
 import ssl as ssl_module
 import threading
 import warnings
-from typing import Any, Optional, Sequence, Type
+from typing import Any, Sequence, Type
 
 from ..client import ClientProtocol
 from ..datastructures import HeadersLike
@@ -52,7 +52,7 @@ def __init__(
         socket: socket.socket,
         protocol: ClientProtocol,
         *,
-        close_timeout: Optional[float] = 10,
+        close_timeout: float | None = 10,
     ) -> None:
         self.protocol: ClientProtocol
         self.response_rcvd = threading.Event()
@@ -64,9 +64,9 @@ def __init__(
 
     def handshake(
         self,
-        additional_headers: Optional[HeadersLike] = None,
-        user_agent_header: Optional[str] = USER_AGENT,
-        timeout: Optional[float] = None,
+        additional_headers: HeadersLike | None = None,
+        user_agent_header: str | None = USER_AGENT,
+        timeout: float | None = None,
     ) -> None:
         """
         Perform the opening handshake.
@@ -128,25 +128,25 @@ def connect(
     uri: str,
     *,
     # TCP/TLS
-    sock: Optional[socket.socket] = None,
-    ssl: Optional[ssl_module.SSLContext] = None,
-    server_hostname: Optional[str] = None,
+    sock: socket.socket | None = None,
+    ssl: ssl_module.SSLContext | None = None,
+    server_hostname: str | None = None,
     # WebSocket
-    origin: Optional[Origin] = None,
-    extensions: Optional[Sequence[ClientExtensionFactory]] = None,
-    subprotocols: Optional[Sequence[Subprotocol]] = None,
-    additional_headers: Optional[HeadersLike] = None,
-    user_agent_header: Optional[str] = USER_AGENT,
-    compression: Optional[str] = "deflate",
+    origin: Origin | None = None,
+    extensions: Sequence[ClientExtensionFactory] | None = None,
+    subprotocols: Sequence[Subprotocol] | None = None,
+    additional_headers: HeadersLike | None = None,
+    user_agent_header: str | None = USER_AGENT,
+    compression: str | None = "deflate",
     # Timeouts
-    open_timeout: Optional[float] = 10,
-    close_timeout: Optional[float] = 10,
+    open_timeout: float | None = 10,
+    close_timeout: float | None = 10,
     # Limits
-    max_size: Optional[int] = 2**20,
+    max_size: int | None = 2**20,
     # Logging
-    logger: Optional[LoggerLike] = None,
+    logger: LoggerLike | None = None,
     # Escape hatch for advanced customization
-    create_connection: Optional[Type[ClientConnection]] = None,
+    create_connection: Type[ClientConnection] | None = None,
     **kwargs: Any,
 ) -> ClientConnection:
     """
@@ -219,7 +219,7 @@ def connect(
 
     # Private APIs for unix_connect()
     unix: bool = kwargs.pop("unix", False)
-    path: Optional[str] = kwargs.pop("path", None)
+    path: str | None = kwargs.pop("path", None)
 
     if unix:
         if path is None and sock is None:
@@ -307,8 +307,8 @@ def connect(
 
 
 def unix_connect(
-    path: Optional[str] = None,
-    uri: Optional[str] = None,
+    path: str | None = None,
+    uri: str | None = None,
     **kwargs: Any,
 ) -> ClientConnection:
     """
diff --git a/src/websockets/sync/connection.py b/src/websockets/sync/connection.py
index b41202dc..bb974318 100644
--- a/src/websockets/sync/connection.py
+++ b/src/websockets/sync/connection.py
@@ -8,7 +8,7 @@
 import threading
 import uuid
 from types import TracebackType
-from typing import Any, Dict, Iterable, Iterator, Mapping, Optional, Type, Union
+from typing import Any, Dict, Iterable, Iterator, Mapping, Type, Union
 
 from ..exceptions import ConnectionClosed, ConnectionClosedOK, ProtocolError
 from ..frames import DATA_OPCODES, BytesLike, CloseCode, Frame, Opcode, prepare_ctrl
@@ -42,7 +42,7 @@ def __init__(
         socket: socket.socket,
         protocol: Protocol,
         *,
-        close_timeout: Optional[float] = 10,
+        close_timeout: float | None = 10,
     ) -> None:
         self.socket = socket
         self.protocol = protocol
@@ -62,9 +62,9 @@ def __init__(
         self.debug = self.protocol.debug
 
         # HTTP handshake request and response.
-        self.request: Optional[Request] = None
+        self.request: Request | None = None
         """Opening handshake request."""
-        self.response: Optional[Response] = None
+        self.response: Response | None = None
         """Opening handshake response."""
 
         # Mutex serializing interactions with the protocol.
@@ -77,7 +77,7 @@ def __init__(
         self.send_in_progress = False
 
         # Deadline for the closing handshake.
-        self.close_deadline: Optional[Deadline] = None
+        self.close_deadline: Deadline | None = None
 
         # Mapping of ping IDs to pong waiters, in chronological order.
         self.ping_waiters: Dict[bytes, threading.Event] = {}
@@ -93,7 +93,7 @@ def __init__(
 
         # Exception raised in recv_events, to be chained to ConnectionClosed
         # in the user thread in order to show why the TCP connection dropped.
-        self.recv_exc: Optional[BaseException] = None
+        self.recv_exc: BaseException | None = None
 
     # Public attributes
 
@@ -124,7 +124,7 @@ def remote_address(self) -> Any:
         return self.socket.getpeername()
 
     @property
-    def subprotocol(self) -> Optional[Subprotocol]:
+    def subprotocol(self) -> Subprotocol | None:
         """
         Subprotocol negotiated during the opening handshake.
 
@@ -140,9 +140,9 @@ def __enter__(self) -> Connection:
 
     def __exit__(
         self,
-        exc_type: Optional[Type[BaseException]],
-        exc_value: Optional[BaseException],
-        traceback: Optional[TracebackType],
+        exc_type: Type[BaseException] | None,
+        exc_value: BaseException | None,
+        traceback: TracebackType | None,
     ) -> None:
         if exc_type is None:
             self.close()
@@ -166,7 +166,7 @@ def __iter__(self) -> Iterator[Data]:
         except ConnectionClosedOK:
             return
 
-    def recv(self, timeout: Optional[float] = None) -> Data:
+    def recv(self, timeout: float | None = None) -> Data:
         """
         Receive the next message.
 
@@ -420,7 +420,7 @@ def close(self, code: int = CloseCode.NORMAL_CLOSURE, reason: str = "") -> None:
             # They mean that the connection is closed, which was the goal.
             pass
 
-    def ping(self, data: Optional[Data] = None) -> threading.Event:
+    def ping(self, data: Data | None = None) -> threading.Event:
         """
         Send a Ping_.
 
@@ -647,7 +647,7 @@ def send_context(
         # Should we close the socket and raise ConnectionClosed?
         raise_close_exc = False
         # What exception should we chain ConnectionClosed to?
-        original_exc: Optional[BaseException] = None
+        original_exc: BaseException | None = None
 
         # Acquire the protocol lock.
         with self.protocol_mutex:
@@ -748,7 +748,7 @@ def send_data(self) -> None:
                 except OSError:  # socket already closed
                     pass
 
-    def set_recv_exc(self, exc: Optional[BaseException]) -> None:
+    def set_recv_exc(self, exc: BaseException | None) -> None:
         """
         Set recv_exc, if not set yet.
 
diff --git a/src/websockets/sync/messages.py b/src/websockets/sync/messages.py
index dcba183d..2c604ba0 100644
--- a/src/websockets/sync/messages.py
+++ b/src/websockets/sync/messages.py
@@ -3,7 +3,7 @@
 import codecs
 import queue
 import threading
-from typing import Iterator, List, Optional, cast
+from typing import Iterator, List, cast
 
 from ..frames import OP_BINARY, OP_CONT, OP_TEXT, Frame
 from ..typing import Data
@@ -41,7 +41,7 @@ def __init__(self) -> None:
         self.put_in_progress = False
 
         # Decoder for text frames, None for binary frames.
-        self.decoder: Optional[codecs.IncrementalDecoder] = None
+        self.decoder: codecs.IncrementalDecoder | None = None
 
         # Buffer of frames belonging to the same message.
         self.chunks: List[Data] = []
@@ -54,12 +54,12 @@ def __init__(self) -> None:
 
         # Stream data from frames belonging to the same message.
         # Remove quotes around type when dropping Python < 3.9.
-        self.chunks_queue: Optional["queue.SimpleQueue[Optional[Data]]"] = None
+        self.chunks_queue: "queue.SimpleQueue[Data | None] | None" = None
 
         # This flag marks the end of the connection.
         self.closed = False
 
-    def get(self, timeout: Optional[float] = None) -> Data:
+    def get(self, timeout: float | None = None) -> Data:
         """
         Read the next message.
 
@@ -151,7 +151,7 @@ def get_iter(self) -> Iterator[Data]:
             self.chunks = []
             self.chunks_queue = cast(
                 # Remove quotes around type when dropping Python < 3.9.
-                "queue.SimpleQueue[Optional[Data]]",
+                "queue.SimpleQueue[Data | None]",
                 queue.SimpleQueue(),
             )
 
@@ -164,7 +164,7 @@ def get_iter(self) -> Iterator[Data]:
             self.get_in_progress = True
 
         # Locking with get_in_progress ensures only one thread can get here.
-        chunk: Optional[Data]
+        chunk: Data | None
         for chunk in chunks:
             yield chunk
         while (chunk := self.chunks_queue.get()) is not None:
diff --git a/src/websockets/sync/server.py b/src/websockets/sync/server.py
index fd4f5d3b..b801510b 100644
--- a/src/websockets/sync/server.py
+++ b/src/websockets/sync/server.py
@@ -10,7 +10,7 @@
 import threading
 import warnings
 from types import TracebackType
-from typing import Any, Callable, Optional, Sequence, Type
+from typing import Any, Callable, Sequence, Type
 
 from ..extensions.base import ServerExtensionFactory
 from ..extensions.permessage_deflate import enable_server_permessage_deflate
@@ -57,7 +57,7 @@ def __init__(
         socket: socket.socket,
         protocol: ServerProtocol,
         *,
-        close_timeout: Optional[float] = 10,
+        close_timeout: float | None = 10,
     ) -> None:
         self.protocol: ServerProtocol
         self.request_rcvd = threading.Event()
@@ -69,20 +69,22 @@ def __init__(
 
     def handshake(
         self,
-        process_request: Optional[
+        process_request: (
             Callable[
                 [ServerConnection, Request],
-                Optional[Response],
+                Response | None,
             ]
-        ] = None,
-        process_response: Optional[
+            | None
+        ) = None,
+        process_response: (
             Callable[
                 [ServerConnection, Request, Response],
-                Optional[Response],
+                Response | None,
             ]
-        ] = None,
-        server_header: Optional[str] = USER_AGENT,
-        timeout: Optional[float] = None,
+            | None
+        ) = None,
+        server_header: str | None = USER_AGENT,
+        timeout: float | None = None,
     ) -> None:
         """
         Perform the opening handshake.
@@ -197,7 +199,7 @@ def __init__(
         self,
         socket: socket.socket,
         handler: Callable[[socket.socket, Any], None],
-        logger: Optional[LoggerLike] = None,
+        logger: LoggerLike | None = None,
     ):
         self.socket = socket
         self.handler = handler
@@ -260,54 +262,57 @@ def __enter__(self) -> WebSocketServer:
 
     def __exit__(
         self,
-        exc_type: Optional[Type[BaseException]],
-        exc_value: Optional[BaseException],
-        traceback: Optional[TracebackType],
+        exc_type: Type[BaseException] | None,
+        exc_value: BaseException | None,
+        traceback: TracebackType | None,
     ) -> None:
         self.shutdown()
 
 
 def serve(
     handler: Callable[[ServerConnection], None],
-    host: Optional[str] = None,
-    port: Optional[int] = None,
+    host: str | None = None,
+    port: int | None = None,
     *,
     # TCP/TLS
-    sock: Optional[socket.socket] = None,
-    ssl: Optional[ssl_module.SSLContext] = None,
+    sock: socket.socket | None = None,
+    ssl: ssl_module.SSLContext | None = None,
     # WebSocket
-    origins: Optional[Sequence[Optional[Origin]]] = None,
-    extensions: Optional[Sequence[ServerExtensionFactory]] = None,
-    subprotocols: Optional[Sequence[Subprotocol]] = None,
-    select_subprotocol: Optional[
+    origins: Sequence[Origin | None] | None = None,
+    extensions: Sequence[ServerExtensionFactory] | None = None,
+    subprotocols: Sequence[Subprotocol] | None = None,
+    select_subprotocol: (
         Callable[
             [ServerConnection, Sequence[Subprotocol]],
-            Optional[Subprotocol],
+            Subprotocol | None,
         ]
-    ] = None,
-    process_request: Optional[
+        | None
+    ) = None,
+    process_request: (
         Callable[
             [ServerConnection, Request],
-            Optional[Response],
+            Response | None,
         ]
-    ] = None,
-    process_response: Optional[
+        | None
+    ) = None,
+    process_response: (
         Callable[
             [ServerConnection, Request, Response],
-            Optional[Response],
+            Response | None,
         ]
-    ] = None,
-    server_header: Optional[str] = USER_AGENT,
-    compression: Optional[str] = "deflate",
+        | None
+    ) = None,
+    server_header: str | None = USER_AGENT,
+    compression: str | None = "deflate",
     # Timeouts
-    open_timeout: Optional[float] = 10,
-    close_timeout: Optional[float] = 10,
+    open_timeout: float | None = 10,
+    close_timeout: float | None = 10,
     # Limits
-    max_size: Optional[int] = 2**20,
+    max_size: int | None = 2**20,
     # Logging
-    logger: Optional[LoggerLike] = None,
+    logger: LoggerLike | None = None,
     # Escape hatch for advanced customization
-    create_connection: Optional[Type[ServerConnection]] = None,
+    create_connection: Type[ServerConnection] | None = None,
     **kwargs: Any,
 ) -> WebSocketServer:
     """
@@ -412,7 +417,7 @@ def handler(websocket):
 
     # Private APIs for unix_connect()
     unix: bool = kwargs.pop("unix", False)
-    path: Optional[str] = kwargs.pop("path", None)
+    path: str | None = kwargs.pop("path", None)
 
     if sock is None:
         if unix:
@@ -460,18 +465,19 @@ def conn_handler(sock: socket.socket, addr: Any) -> None:
                 sock.settimeout(None)
 
             # Create a closure to give select_subprotocol access to connection.
-            protocol_select_subprotocol: Optional[
+            protocol_select_subprotocol: (
                 Callable[
                     [ServerProtocol, Sequence[Subprotocol]],
-                    Optional[Subprotocol],
+                    Subprotocol | None,
                 ]
-            ] = None
+                | None
+            ) = None
             if select_subprotocol is not None:
 
                 def protocol_select_subprotocol(
                     protocol: ServerProtocol,
                     subprotocols: Sequence[Subprotocol],
-                ) -> Optional[Subprotocol]:
+                ) -> Subprotocol | None:
                     # mypy doesn't know that select_subprotocol is immutable.
                     assert select_subprotocol is not None
                     # Ensure this function is only used in the intended context.
@@ -525,7 +531,7 @@ def protocol_select_subprotocol(
 
 def unix_serve(
     handler: Callable[[ServerConnection], None],
-    path: Optional[str] = None,
+    path: str | None = None,
     **kwargs: Any,
 ) -> WebSocketServer:
     """
diff --git a/src/websockets/sync/utils.py b/src/websockets/sync/utils.py
index 3364bdc2..00bce2cc 100644
--- a/src/websockets/sync/utils.py
+++ b/src/websockets/sync/utils.py
@@ -1,7 +1,6 @@
 from __future__ import annotations
 
 import time
-from typing import Optional
 
 
 __all__ = ["Deadline"]
@@ -16,14 +15,14 @@ class Deadline:
 
     """
 
-    def __init__(self, timeout: Optional[float]) -> None:
-        self.deadline: Optional[float]
+    def __init__(self, timeout: float | None) -> None:
+        self.deadline: float | None
         if timeout is None:
             self.deadline = None
         else:
             self.deadline = time.monotonic() + timeout
 
-    def timeout(self, *, raise_if_elapsed: bool = True) -> Optional[float]:
+    def timeout(self, *, raise_if_elapsed: bool = True) -> float | None:
         """
         Calculate a timeout from a deadline.
 
diff --git a/src/websockets/typing.py b/src/websockets/typing.py
index 5dfecf66..7c5b3664 100644
--- a/src/websockets/typing.py
+++ b/src/websockets/typing.py
@@ -53,7 +53,7 @@
 ExtensionName = NewType("ExtensionName", str)
 """Name of a WebSocket extension."""
 
-
+# Change to str | None when dropping Python < 3.10.
 ExtensionParameter = Tuple[str, Optional[str]]
 """Parameter of a WebSocket extension."""
 
diff --git a/src/websockets/uri.py b/src/websockets/uri.py
index 8cf58174..90271606 100644
--- a/src/websockets/uri.py
+++ b/src/websockets/uri.py
@@ -2,7 +2,7 @@
 
 import dataclasses
 import urllib.parse
-from typing import Optional, Tuple
+from typing import Tuple
 
 from . import exceptions
 
@@ -33,8 +33,8 @@ class WebSocketURI:
     port: int
     path: str
     query: str
-    username: Optional[str] = None
-    password: Optional[str] = None
+    username: str | None = None
+    password: str | None = None
 
     @property
     def resource_name(self) -> str:
@@ -47,7 +47,7 @@ def resource_name(self) -> str:
         return resource_name
 
     @property
-    def user_info(self) -> Optional[Tuple[str, str]]:
+    def user_info(self) -> Tuple[str, str] | None:
         if self.username is None:
             return None
         assert self.password is not None