diff --git a/Doc/c-api/sys.rst b/Doc/c-api/sys.rst
index c6777d6..95d9d65 100644
--- a/Doc/c-api/sys.rst
+++ b/Doc/c-api/sys.rst
@@ -49,9 +49,10 @@
 
 .. c:function:: void PyOS_AfterFork_Child()
 
-   Function to update some internal state after a process fork.  This
-   should be called from the child process after calling :c:func:`fork`
-   or any similar function that clones the current process.
+   Function to update internal interpreter state after a process fork.
+   This must be called from the child process after calling :c:func:`fork`,
+   or any similar function that clones the current process, if there is
+   any chance the process will call back into the Python interpreter.
    Only available on systems where :c:func:`fork` is defined.
 
    .. versionadded:: 3.7
diff --git a/Doc/library/os.rst b/Doc/library/os.rst
index 28921ad..86add0c 100644
--- a/Doc/library/os.rst
+++ b/Doc/library/os.rst
@@ -3280,16 +3280,22 @@
    subprocesses.
 
 
-.. function:: register_at_fork(func, when)
+.. function:: register_at_fork(*, before=None, after_in_parent=None, \
+                               after_in_child=None)
 
-   Register *func* as a function to be executed when a new child process
-   is forked.  *when* is a string specifying at which point the function is
-   called and can take the following values:
+   Register callables to be executed when a new child process is forked
+   using :func:`os.fork` or similar process cloning APIs.
+   The parameters are optional and keyword-only.
+   Each specifies a different call point.
 
-   * *"before"* means the function is called before forking a child process;
-   * *"parent"* means the function is called from the parent process after
-     forking a child process;
-   * *"child"* means the function is called from the child process.
+   * *before* is a function called before forking a child process.
+   * *after_in_parent* is a function called from the parent process
+     after forking a child process.
+   * *after_in_child* is a function called from the child process.
+
+   These calls are only made if control is expected to return to the
+   Python interpreter.  A typical :mod:`subprocess` launch will not
+   trigger them as the child is not going to re-enter the interpreter.
 
    Functions registered for execution before forking are called in
    reverse registration order.  Functions registered for execution
@@ -3300,6 +3306,8 @@
    call those functions, unless it explicitly calls :c:func:`PyOS_BeforeFork`,
    :c:func:`PyOS_AfterFork_Parent` and :c:func:`PyOS_AfterFork_Child`.
 
+   There is no way to unregister a function.
+
    Availability: Unix.
 
    .. versionadded:: 3.7