diff --git a/trio/_channel.py b/trio/_channel.py
index 1cecc55621..f3fef1699e 100644
--- a/trio/_channel.py
+++ b/trio/_channel.py
@@ -1,6 +1,19 @@
+from __future__ import annotations
+
 from collections import deque, OrderedDict
+from collections.abc import Callable
 from math import inf
 
+from types import TracebackType
+from typing import (
+    Any,
+    Generic,
+    NoReturn,
+    TypeVar,
+    TYPE_CHECKING,
+    Tuple,  # only needed for typechecking on <3.9
+)
+
 import attr
 from outcome import Error, Value
 
@@ -8,11 +21,29 @@
 from ._util import generic_function, NoPublicConstructor
 
 import trio
-from ._core import enable_ki_protection
+from ._core import enable_ki_protection, Task, Abort
+from ._core._traps import _RaiseCancelT
+
+# A regular invariant generic type
+T = TypeVar("T")
+
+# The type of object produced by a ReceiveChannel (covariant because
+# ReceiveChannel[Derived] can be passed to someone expecting
+# ReceiveChannel[Base])
+ReceiveType = TypeVar("ReceiveType", covariant=True)
+
+# The type of object accepted by a SendChannel (contravariant because
+# SendChannel[Base] can be passed to someone expecting
+# SendChannel[Derived])
+SendType = TypeVar("SendType", contravariant=True)
 
+# Temporary TypeVar needed until mypy release supports Self as a type
+SelfT = TypeVar("SelfT")
 
-@generic_function
-def open_memory_channel(max_buffer_size):
+
+def _open_memory_channel(
+    max_buffer_size: int,
+) -> tuple[MemorySendChannel[T], MemoryReceiveChannel[T]]:
     """Open a channel for passing objects between tasks within a process.
 
     Memory channels are lightweight, cheap to allocate, and entirely
@@ -68,36 +99,57 @@ def open_memory_channel(max_buffer_size):
         raise TypeError("max_buffer_size must be an integer or math.inf")
     if max_buffer_size < 0:
         raise ValueError("max_buffer_size must be >= 0")
-    state = MemoryChannelState(max_buffer_size)
+    state: MemoryChannelState[T] = MemoryChannelState(max_buffer_size)
     return (
-        MemorySendChannel._create(state),
-        MemoryReceiveChannel._create(state),
+        MemorySendChannel[T]._create(state),
+        MemoryReceiveChannel[T]._create(state),
     )
 
 
+# This workaround requires python3.9+, once older python versions are not supported
+# or there's a better way of achieving type-checking on a generic factory function,
+# it could replace the normal function header
+if TYPE_CHECKING:
+    # written as a class so you can say open_memory_channel[int](5)
+    # Need to use Tuple instead of tuple due to CI check running on 3.8
+    class open_memory_channel(Tuple[MemorySendChannel[T], MemoryReceiveChannel[T]]):
+        def __new__(  # type: ignore[misc]  # "must return a subtype"
+            cls, max_buffer_size: int
+        ) -> tuple[MemorySendChannel[T], MemoryReceiveChannel[T]]:
+            return _open_memory_channel(max_buffer_size)
+
+        def __init__(self, max_buffer_size: int):
+            ...
+
+else:
+    # apply the generic_function decorator to make open_memory_channel indexable
+    # so it's valid to say e.g. ``open_memory_channel[bytes](5)`` at runtime
+    open_memory_channel = generic_function(_open_memory_channel)
+
+
 @attr.s(frozen=True, slots=True)
 class MemoryChannelStats:
-    current_buffer_used = attr.ib()
-    max_buffer_size = attr.ib()
-    open_send_channels = attr.ib()
-    open_receive_channels = attr.ib()
-    tasks_waiting_send = attr.ib()
-    tasks_waiting_receive = attr.ib()
+    current_buffer_used: int = attr.ib()
+    max_buffer_size: int = attr.ib()
+    open_send_channels: int = attr.ib()
+    open_receive_channels: int = attr.ib()
+    tasks_waiting_send: int = attr.ib()
+    tasks_waiting_receive: int = attr.ib()
 
 
 @attr.s(slots=True)
-class MemoryChannelState:
-    max_buffer_size = attr.ib()
-    data = attr.ib(factory=deque)
+class MemoryChannelState(Generic[T]):
+    max_buffer_size: int = attr.ib()
+    data: deque[T] = attr.ib(factory=deque)
     # Counts of open endpoints using this state
-    open_send_channels = attr.ib(default=0)
-    open_receive_channels = attr.ib(default=0)
+    open_send_channels: int = attr.ib(default=0)
+    open_receive_channels: int = attr.ib(default=0)
     # {task: value}
-    send_tasks = attr.ib(factory=OrderedDict)
+    send_tasks: OrderedDict[Task, T] = attr.ib(factory=OrderedDict)
     # {task: None}
-    receive_tasks = attr.ib(factory=OrderedDict)
+    receive_tasks: OrderedDict[Task, None] = attr.ib(factory=OrderedDict)
 
-    def statistics(self):
+    def statistics(self) -> MemoryChannelStats:
         return MemoryChannelStats(
             current_buffer_used=len(self.data),
             max_buffer_size=self.max_buffer_size,
@@ -109,28 +161,28 @@ def statistics(self):
 
 
 @attr.s(eq=False, repr=False)
-class MemorySendChannel(SendChannel, metaclass=NoPublicConstructor):
-    _state = attr.ib()
-    _closed = attr.ib(default=False)
+class MemorySendChannel(SendChannel[SendType], metaclass=NoPublicConstructor):
+    _state: MemoryChannelState[SendType] = attr.ib()
+    _closed: bool = attr.ib(default=False)
     # This is just the tasks waiting on *this* object. As compared to
     # self._state.send_tasks, which includes tasks from this object and
     # all clones.
-    _tasks = attr.ib(factory=set)
+    _tasks: set[Task] = attr.ib(factory=set)
 
-    def __attrs_post_init__(self):
+    def __attrs_post_init__(self) -> None:
         self._state.open_send_channels += 1
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         return "<send channel at {:#x}, using buffer at {:#x}>".format(
             id(self), id(self._state)
         )
 
-    def statistics(self):
+    def statistics(self) -> MemoryChannelStats:
         # XX should we also report statistics specific to this object?
         return self._state.statistics()
 
     @enable_ki_protection
-    def send_nowait(self, value):
+    def send_nowait(self, value: SendType) -> None:
         """Like `~trio.abc.SendChannel.send`, but if the channel's buffer is
         full, raises `WouldBlock` instead of blocking.
 
@@ -150,7 +202,7 @@ def send_nowait(self, value):
             raise trio.WouldBlock
 
     @enable_ki_protection
-    async def send(self, value):
+    async def send(self, value: SendType) -> None:
         """See `SendChannel.send <trio.abc.SendChannel.send>`.
 
         Memory channels allow multiple tasks to call `send` at the same time.
@@ -170,15 +222,16 @@ async def send(self, value):
         self._state.send_tasks[task] = value
         task.custom_sleep_data = self
 
-        def abort_fn(_):
+        def abort_fn(_: _RaiseCancelT) -> Abort:
             self._tasks.remove(task)
             del self._state.send_tasks[task]
             return trio.lowlevel.Abort.SUCCEEDED
 
         await trio.lowlevel.wait_task_rescheduled(abort_fn)
 
+    # Return type must be stringified or use a TypeVar
     @enable_ki_protection
-    def clone(self):
+    def clone(self) -> "MemorySendChannel[SendType]":
         """Clone this send channel object.
 
         This returns a new `MemorySendChannel` object, which acts as a
@@ -206,14 +259,19 @@ def clone(self):
             raise trio.ClosedResourceError
         return MemorySendChannel._create(self._state)
 
-    def __enter__(self):
+    def __enter__(self: SelfT) -> SelfT:
         return self
 
-    def __exit__(self, exc_type, exc_val, exc_tb):
+    def __exit__(
+        self,
+        exc_type: type[BaseException] | None,
+        exc_val: BaseException | None,
+        exc_tb: TracebackType | None,
+    ) -> None:
         self.close()
 
     @enable_ki_protection
-    def close(self):
+    def close(self) -> None:
         """Close this send channel object synchronously.
 
         All channel objects have an asynchronous `~.AsyncResource.aclose` method.
@@ -241,30 +299,30 @@ def close(self):
             self._state.receive_tasks.clear()
 
     @enable_ki_protection
-    async def aclose(self):
+    async def aclose(self) -> None:
         self.close()
         await trio.lowlevel.checkpoint()
 
 
 @attr.s(eq=False, repr=False)
-class MemoryReceiveChannel(ReceiveChannel, metaclass=NoPublicConstructor):
-    _state = attr.ib()
-    _closed = attr.ib(default=False)
-    _tasks = attr.ib(factory=set)
+class MemoryReceiveChannel(ReceiveChannel[ReceiveType], metaclass=NoPublicConstructor):
+    _state: MemoryChannelState[ReceiveType] = attr.ib()
+    _closed: bool = attr.ib(default=False)
+    _tasks: set[trio._core._run.Task] = attr.ib(factory=set)
 
-    def __attrs_post_init__(self):
+    def __attrs_post_init__(self) -> None:
         self._state.open_receive_channels += 1
 
-    def statistics(self):
+    def statistics(self) -> MemoryChannelStats:
         return self._state.statistics()
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         return "<receive channel at {:#x}, using buffer at {:#x}>".format(
             id(self), id(self._state)
         )
 
     @enable_ki_protection
-    def receive_nowait(self):
+    def receive_nowait(self) -> ReceiveType:
         """Like `~trio.abc.ReceiveChannel.receive`, but if there's nothing
         ready to receive, raises `WouldBlock` instead of blocking.
 
@@ -284,7 +342,7 @@ def receive_nowait(self):
         raise trio.WouldBlock
 
     @enable_ki_protection
-    async def receive(self):
+    async def receive(self) -> ReceiveType:
         """See `ReceiveChannel.receive <trio.abc.ReceiveChannel.receive>`.
 
         Memory channels allow multiple tasks to call `receive` at the same
@@ -306,15 +364,17 @@ async def receive(self):
         self._state.receive_tasks[task] = None
         task.custom_sleep_data = self
 
-        def abort_fn(_):
+        def abort_fn(_: _RaiseCancelT) -> Abort:
             self._tasks.remove(task)
             del self._state.receive_tasks[task]
             return trio.lowlevel.Abort.SUCCEEDED
 
-        return await trio.lowlevel.wait_task_rescheduled(abort_fn)
+        # Not strictly guaranteed to return ReceiveType, but will do so unless
+        # you intentionally reschedule with a bad value.
+        return await trio.lowlevel.wait_task_rescheduled(abort_fn)  # type: ignore[no-any-return]
 
     @enable_ki_protection
-    def clone(self):
+    def clone(self) -> "MemoryReceiveChannel[ReceiveType]":
         """Clone this receive channel object.
 
         This returns a new `MemoryReceiveChannel` object, which acts as a
@@ -345,14 +405,19 @@ def clone(self):
             raise trio.ClosedResourceError
         return MemoryReceiveChannel._create(self._state)
 
-    def __enter__(self):
+    def __enter__(self: SelfT) -> SelfT:
         return self
 
-    def __exit__(self, exc_type, exc_val, exc_tb):
+    def __exit__(
+        self,
+        exc_type: type[BaseException] | None,
+        exc_val: BaseException | None,
+        exc_tb: TracebackType | None,
+    ) -> None:
         self.close()
 
     @enable_ki_protection
-    def close(self):
+    def close(self) -> None:
         """Close this receive channel object synchronously.
 
         All channel objects have an asynchronous `~.AsyncResource.aclose` method.
@@ -381,6 +446,6 @@ def close(self):
             self._state.data.clear()
 
     @enable_ki_protection
-    async def aclose(self):
+    async def aclose(self) -> None:
         self.close()
         await trio.lowlevel.checkpoint()
diff --git a/trio/_core/_traps.py b/trio/_core/_traps.py
index 95cf46de9b..7611894ce2 100644
--- a/trio/_core/_traps.py
+++ b/trio/_core/_traps.py
@@ -8,6 +8,7 @@
 
 from . import _run
 
+from typing import Callable, NoReturn, Any
 
 # Helper for the bottommost 'yield'. You can't use 'yield' inside an async
 # function, but you can inside a generator, and if you decorate your generator
@@ -64,7 +65,11 @@ class WaitTaskRescheduled:
     abort_func = attr.ib()
 
 
-async def wait_task_rescheduled(abort_func):
+_RaiseCancelT = Callable[[], NoReturn]  # TypeAlias
+
+# Should always return the type a Task "expects", unless you willfully reschedule it
+# with a bad value.
+async def wait_task_rescheduled(abort_func: Callable[[_RaiseCancelT], Abort]) -> Any:
     """Put the current task to sleep, with cancellation support.
 
     This is the lowest-level API for blocking in Trio. Every time a