diff --git a/docs/source/conf.py b/docs/source/conf.py
index eb278bf65f..46a3f6bae3 100755
--- a/docs/source/conf.py
+++ b/docs/source/conf.py
@@ -173,7 +173,6 @@ def autodoc_process_signature(
 # currently undocumented things
 logger = getLogger("trio")
 UNDOCUMENTED = {
-    "trio._subprocess.HasFileno.fileno",
     "trio.lowlevel.ParkingLot.broken_by",
 }
 
diff --git a/newsfragments/3226.bugfix.rst b/newsfragments/3226.bugfix.rst
new file mode 100644
index 0000000000..6a79334f25
--- /dev/null
+++ b/newsfragments/3226.bugfix.rst
@@ -0,0 +1 @@
+Add docstrings that ``pyright --verifytypes`` complains about.
diff --git a/src/trio/_core/_io_epoll.py b/src/trio/_core/_io_epoll.py
index d7064dc718..7ab3f3aca8 100644
--- a/src/trio/_core/_io_epoll.py
+++ b/src/trio/_core/_io_epoll.py
@@ -33,6 +33,32 @@ class EpollWaiters:
 
 @attrs.frozen(eq=False)
 class _EpollStatistics:
+    """DTO class that holds information on current epoll status.
+
+    This class can be used on any platform that supports
+    epoll functionality (e.g. Linux).
+    Trio also defines other similar classes for statistics reporting:
+    ``_WindowsStatistics`` and ``_KqueueStatistics``.
+    They are similar in function but some fields differ.
+    All of them have a ``backend`` attribute.
+    The statistics class best suited for the runtime platform is
+    imported as the ``IOStatistics`` type. See ``trio._core._run``.
+
+    .. attribute:: tasks_waiting_read
+
+       Number of tasks waiting on read.
+
+    .. attribute:: tasks_waiting_write
+
+       Number of tasks waiting on write.
+
+    .. attribute:: backend
+
+       This attribute holds a string value that corresponds to the statistics type.
+       This class has ``backend == "epoll"``.
+       Use ``backend`` attribute to distinguish statistics types at runtime.
+    """
+
     tasks_waiting_read: int
     tasks_waiting_write: int
     backend: Literal["epoll"] = attrs.field(init=False, default="epoll")
diff --git a/src/trio/_core/_io_kqueue.py b/src/trio/_core/_io_kqueue.py
index 80d0ce6296..514434f16d 100644
--- a/src/trio/_core/_io_kqueue.py
+++ b/src/trio/_core/_io_kqueue.py
@@ -26,6 +26,32 @@
 
 @attrs.frozen(eq=False)
 class _KqueueStatistics:
+    """DTO class that holds information on current kqueue status.
+
+    This class can be used on any platform that supports
+    kqueue functionality (e.g. BSD/Darwin).
+    Trio also defines other similar classes for statistics reporting:
+    ``_WindowsStatistics`` and ``_EpollStatistics``.
+    They are similar in function but some fields differ.
+    All of them have a ``backend`` attribute.
+    The statistics class best suited for the runtime platform is
+    imported as the ``IOStatistics`` type. See ``trio._core._run``.
+
+    .. attribute:: tasks_waiting
+
+       Number of tasks that are currently in the waiting state.
+
+    .. attribute:: monitors
+
+       Number of monitors.
+
+    .. attribute:: backend
+
+       This attribute holds a string value that corresponds to the statistics type.
+       This class has ``backend == "kqueue"``.
+       Use ``backend`` attribute to distinguish statistics types at runtime.
+    """
+
     tasks_waiting: int
     monitors: int
     backend: Literal["kqueue"] = attrs.field(init=False, default="kqueue")
diff --git a/src/trio/_core/_io_windows.py b/src/trio/_core/_io_windows.py
index 7b789c3dec..9c3403d937 100644
--- a/src/trio/_core/_io_windows.py
+++ b/src/trio/_core/_io_windows.py
@@ -293,6 +293,39 @@ class AFDGroup:
 
 @attrs.frozen(eq=False)
 class _WindowsStatistics:
+    """DTO class that holds information on current I/O waits status.
+
+    This class is used on the Windows platform.
+    Trio also defines other similar classes for statistics reporting:
+    ``_KqueueStatistics`` and ``_EpollStatistics``.
+    They are similar in function but some fields differ.
+    All of them have a ``backend`` attribute.
+    The statistics class best suited for the runtime platform is
+    imported as the ``IOStatistics`` type. See ``trio._core._run``.
+
+    .. attribute:: tasks_waiting_read
+
+       Number of tasks waiting on read.
+
+    .. attribute:: tasks_waiting_write
+
+       Number of tasks waiting on write.
+
+    .. attribute:: tasks_waiting_overlapped
+
+       Number of tasks waiting on overlapped I/O operations.
+
+    .. attribute:: completion_key_monitors
+
+       Number of completion key monitors.
+
+    .. attribute:: backend
+
+       This attribute holds a string value that corresponds to the statistics type.
+       This class has ``backend == "windows"``.
+       Use ``backend`` attribute to distinguish statistics types at runtime.
+    """
+
     tasks_waiting_read: int
     tasks_waiting_write: int
     tasks_waiting_overlapped: int
diff --git a/src/trio/_core/_local.py b/src/trio/_core/_local.py
index 21bb913cd9..5d7885eb33 100644
--- a/src/trio/_core/_local.py
+++ b/src/trio/_core/_local.py
@@ -12,7 +12,13 @@
 
 
 @final
-class _NoValue: ...
+class _NoValue:
+    """Sentinel class object, used as the "undefined" variable value.
+
+    A :class:`~trio.lowlevel.RunVar` variable has this "stub" value
+    until the variable is assigned an actual value.
+    It is distinct from ``None``, which is a legitimate value a variable can hold.
+    """
 
 
 @final
diff --git a/src/trio/_core/_run.py b/src/trio/_core/_run.py
index ddd4ea7ee2..93dca680d0 100644
--- a/src/trio/_core/_run.py
+++ b/src/trio/_core/_run.py
@@ -1486,6 +1486,17 @@ def __del__(self) -> None:
 @final
 @attrs.define(eq=False, repr=False)
 class Task(metaclass=NoPublicConstructor):  # type: ignore[explicit-any]
+    """A ``Task`` object represents a concurrent "thread" of execution.
+
+    See the :class:`~trio.lowlevel.Task` entry in Trio's lowlevel module docs for a detailed description.
+    Trio's task primitive wraps a coroutine (`types.CoroutineType`),
+    adding more functionality for stopping and resuming tasks,
+    for scheduling and canceling tasks,
+    for associating a ``Task`` with a ``Runner`` and context variables.
+    A ``Task`` can belong to a :class:`~trio.Nursery` and can spawn
+    its own child nurseries. See :class:`~trio.Nursery` docs for more information.
+    """
+
     _parent_nursery: Nursery | None
     coro: types.CoroutineType[Any, Outcome[object], Any]  # type: ignore[explicit-any]
     _runner: Runner
diff --git a/src/trio/_file_io.py b/src/trio/_file_io.py
index d9305ef4ff..a947d9c04f 100644
--- a/src/trio/_file_io.py
+++ b/src/trio/_file_io.py
@@ -114,7 +114,10 @@ class _HasErrors(Protocol):
         def errors(self) -> str | None: ...
 
     class _HasFileNo(Protocol):
-        def fileno(self) -> int: ...
+        """Represents any file-like object that has a file descriptor."""
+
+        def fileno(self) -> int:
+            """Return the file descriptor."""
 
     class _HasIsATTY(Protocol):
         def isatty(self) -> bool: ...
diff --git a/src/trio/_socket.py b/src/trio/_socket.py
index 504874553a..36a84c96a5 100644
--- a/src/trio/_socket.py
+++ b/src/trio/_socket.py
@@ -544,6 +544,11 @@ async def _resolve_address_nocp(
 
 
 class SocketType:
+    """Trio's version of the standard library's :class:`socket.socket`.
+
+    Encompasses some Trio-specific platform handling logic.
+    """
+
     def __init__(self) -> None:
         # make sure this __init__ works with multiple inheritance
         super().__init__()
diff --git a/src/trio/_subprocess.py b/src/trio/_subprocess.py
index d73ba3dc23..4bb7018e8e 100644
--- a/src/trio/_subprocess.py
+++ b/src/trio/_subprocess.py
@@ -98,7 +98,9 @@ def pidfd_open(fd: int, flags: int) -> int:
 class HasFileno(Protocol):
     """Represents any file-like object that has a file descriptor."""
 
-    def fileno(self) -> int: ...
+    def fileno(self) -> int:
+        """Return the file descriptor."""
+        ...
 
 
 @final
diff --git a/src/trio/_sync.py b/src/trio/_sync.py
index 75d3be721a..90cdac30f6 100644
--- a/src/trio/_sync.py
+++ b/src/trio/_sync.py
@@ -122,12 +122,27 @@ def __bool__(self) -> Literal[True]:
 class _HasAcquireRelease(Protocol):
     """Only classes with acquire() and release() can use the mixin's implementations."""
 
-    async def acquire(self) -> object: ...
+    async def acquire(self) -> object:
+        """Acquire the resource (lock).
 
-    def release(self) -> object: ...
+        See docs for :class:`~trio.Lock` and :class:`~trio.StrictFIFOLock` for usage details.
+        """
+
+    def release(self) -> object:
+        """Release the resource (unlock).
+
+        See docs for :class:`~trio.Lock` and :class:`~trio.StrictFIFOLock` for usage details.
+        """
 
 
 class AsyncContextManagerMixin:
+    """An async context manager base class.
+
+    Should be used with the ``_HasAcquireRelease`` Protocol.
+    Calls ``await self.acquire()`` on entry and ``self.release()`` on exit,
+    adding :exc:`KeyboardInterrupt` protection support.
+    """
+
     @enable_ki_protection
     async def __aenter__(self: _HasAcquireRelease) -> None:
         await self.acquire()
diff --git a/src/trio/_tests/_check_type_completeness.json b/src/trio/_tests/_check_type_completeness.json
index d8a2948cd9..ee3668aca4 100644
--- a/src/trio/_tests/_check_type_completeness.json
+++ b/src/trio/_tests/_check_type_completeness.json
@@ -1,24 +1,6 @@
 {
-    "Darwin": [
-        "No docstring found for function \"trio._unix_pipes.FdStream.close\"",
-        "No docstring found for function \"trio._unix_pipes.FdStream.fileno\""
-    ],
-    "Linux": [
-        "No docstring found for class \"trio._core._io_epoll._EpollStatistics\"",
-        "No docstring found for function \"trio._unix_pipes.FdStream.close\"",
-        "No docstring found for function \"trio._unix_pipes.FdStream.fileno\""
-    ],
+    "Darwin": [],
+    "Linux": [],
     "Windows": [],
-    "all": [
-        "No docstring found for class \"trio._core._run.Task\"",
-        "No docstring found for class \"trio._socket.SocketType\"",
-        "No docstring found for function \"trio._subprocess.HasFileno.fileno\"",
-        "No docstring found for class \"trio._sync.AsyncContextManagerMixin\"",
-        "No docstring found for function \"trio._sync._HasAcquireRelease.acquire\"",
-        "No docstring found for function \"trio._sync._HasAcquireRelease.release\"",
-        "No docstring found for class \"trio._sync._LockImpl\"",
-        "No docstring found for class \"trio._core._local._NoValue\"",
-        "No docstring found for class \"trio.lowlevel.Task\"",
-        "No docstring found for class \"trio.socket.SocketType\""
-    ]
+    "all": []
 }
diff --git a/src/trio/_tests/check_type_completeness.py b/src/trio/_tests/check_type_completeness.py
index bbf38080d3..c6911da357 100755
--- a/src/trio/_tests/check_type_completeness.py
+++ b/src/trio/_tests/check_type_completeness.py
@@ -74,30 +74,16 @@ def has_docstring_at_runtime(name: str) -> bool:
             # on separate platforms. It might also be a decent idea to work the other way around,
             # a la test_static_tool_sees_class_members
             # darwin
-            "trio.lowlevel.current_kqueue",
-            "trio.lowlevel.monitor_kevent",
-            "trio.lowlevel.wait_kevent",
             "trio._core._io_kqueue._KqueueStatistics",
             # windows
             "trio._socket.SocketType.share",
             "trio._core._io_windows._WindowsStatistics",
             "trio._core._windows_cffi.Handle",
-            "trio.lowlevel.current_iocp",
-            "trio.lowlevel.monitor_completion_key",
-            "trio.lowlevel.readinto_overlapped",
-            "trio.lowlevel.register_with_iocp",
-            "trio.lowlevel.wait_overlapped",
-            "trio.lowlevel.write_overlapped",
-            "trio.lowlevel.WaitForSingleObject",
-            "trio.socket.fromshare",
             # linux
             # this test will fail on linux, but I don't develop on linux. So the next
             # person to do so is very welcome to open a pull request and populate with
             # objects
             # TODO: these are erroring on all platforms, why?
-            "trio._highlevel_generic.StapledStream.send_stream",
-            "trio._highlevel_generic.StapledStream.receive_stream",
-            "trio._ssl.SSLStream.transport_stream",
             "trio._file_io._HasFileNo",
             "trio._file_io._HasFileNo.fileno",
         ):
diff --git a/src/trio/_unix_pipes.py b/src/trio/_unix_pipes.py
index 598feb61e2..167dd56098 100644
--- a/src/trio/_unix_pipes.py
+++ b/src/trio/_unix_pipes.py
@@ -187,11 +187,23 @@ async def receive_some(self, max_bytes: int | None = None) -> bytes:
             return data
 
     def close(self) -> None:
+        """Close the stream and close file descriptor it's wrapping.
+
+        See the class docstring for details.
+        """
         self._fd_holder.close()
 
     async def aclose(self) -> None:
+        """Close the stream synchronously, then execute a checkpoint.
+
+        See the class docstring for details.
+        """
         self.close()
         await trio.lowlevel.checkpoint()
 
     def fileno(self) -> int:
+        """Return the file descriptor this `FdStream` is wrapping.
+
+        See the class docstring for details.
+        """
         return self._fd_holder.fd