diff --git a/setup.py b/setup.py
index 3b8d32e16..eac568110 100644
--- a/setup.py
+++ b/setup.py
@@ -39,7 +39,7 @@ def get_long_description():
     include_package_data=True,
     install_requires=[
         "anyio>=3.0.0,<4",
-        "typing_extensions; python_version < '3.8'",
+        "typing_extensions; python_version < '3.10'",
         "contextlib2 >= 21.6.0; python_version < '3.7'",
     ],
     extras_require={
diff --git a/starlette/background.py b/starlette/background.py
index 1160baeed..14a4e9e1a 100644
--- a/starlette/background.py
+++ b/starlette/background.py
@@ -1,12 +1,20 @@
 import asyncio
+import sys
 import typing
 
+if sys.version_info >= (3, 10):  # pragma: no cover
+    from typing import ParamSpec
+else:  # pragma: no cover
+    from typing_extensions import ParamSpec
+
 from starlette.concurrency import run_in_threadpool
 
+P = ParamSpec("P")
+
 
 class BackgroundTask:
     def __init__(
-        self, func: typing.Callable, *args: typing.Any, **kwargs: typing.Any
+        self, func: typing.Callable[P, typing.Any], *args: P.args, **kwargs: P.kwargs
     ) -> None:
         self.func = func
         self.args = args
@@ -25,7 +33,7 @@ def __init__(self, tasks: typing.Sequence[BackgroundTask] = None):
         self.tasks = list(tasks) if tasks else []
 
     def add_task(
-        self, func: typing.Callable, *args: typing.Any, **kwargs: typing.Any
+        self, func: typing.Callable[P, typing.Any], *args: P.args, **kwargs: P.kwargs
     ) -> None:
         task = BackgroundTask(func, *args, **kwargs)
         self.tasks.append(task)
diff --git a/starlette/concurrency.py b/starlette/concurrency.py
index e89d1e047..78602077a 100644
--- a/starlette/concurrency.py
+++ b/starlette/concurrency.py
@@ -1,9 +1,14 @@
 import functools
+import sys
 import typing
-from typing import Any, AsyncGenerator, Iterator
 
 import anyio
 
+if sys.version_info >= (3, 10):  # pragma: no cover
+    from typing import ParamSpec
+else:  # pragma: no cover
+    from typing_extensions import ParamSpec
+
 try:
     import contextvars  # Python 3.7+ only or via contextvars backport.
 except ImportError:  # pragma: no cover
@@ -11,6 +16,7 @@
 
 
 T = typing.TypeVar("T")
+P = ParamSpec("P")
 
 
 async def run_until_first_complete(*args: typing.Tuple[typing.Callable, dict]) -> None:
@@ -25,14 +31,14 @@ async def run(func: typing.Callable[[], typing.Coroutine]) -> None:
 
 
 async def run_in_threadpool(
-    func: typing.Callable[..., T], *args: typing.Any, **kwargs: typing.Any
+    func: typing.Callable[P, T], *args: P.args, **kwargs: P.kwargs
 ) -> T:
     if contextvars is not None:  # pragma: no cover
         # Ensure we run in the same context
         child = functools.partial(func, *args, **kwargs)
         context = contextvars.copy_context()
-        func = context.run
-        args = (child,)
+        func = context.run  # type: ignore[assignment]
+        args = (child,)  # type: ignore[assignment]
     elif kwargs:  # pragma: no cover
         # run_sync doesn't accept 'kwargs', so bind them in here
         func = functools.partial(func, **kwargs)
@@ -43,7 +49,7 @@ class _StopIteration(Exception):
     pass
 
 
-def _next(iterator: Iterator) -> Any:
+def _next(iterator: typing.Iterator[T]) -> T:
     # We can't raise `StopIteration` from within the threadpool iterator
     # and catch it outside that context, so we coerce them into a different
     # exception type.
@@ -53,7 +59,9 @@ def _next(iterator: Iterator) -> Any:
         raise _StopIteration
 
 
-async def iterate_in_threadpool(iterator: Iterator) -> AsyncGenerator:
+async def iterate_in_threadpool(
+    iterator: typing.Iterator[T],
+) -> typing.AsyncIterator[T]:
     while True:
         try:
             yield await anyio.to_thread.run_sync(_next, iterator)
diff --git a/starlette/endpoints.py b/starlette/endpoints.py
index e0b7be8de..e27e4fe49 100644
--- a/starlette/endpoints.py
+++ b/starlette/endpoints.py
@@ -29,7 +29,9 @@ async def dispatch(self) -> None:
             else request.method.lower()
         )
 
-        handler = getattr(self, handler_name, self.method_not_allowed)
+        handler: typing.Callable[[Request], typing.Any] = getattr(
+            self, handler_name, self.method_not_allowed
+        )
         is_async = asyncio.iscoroutinefunction(handler)
         if is_async:
             response = await handler(request)