diff --git a/Doc/glossary.rst b/Doc/glossary.rst
index 8af4373b11d7c9e..ed588612aeabed2 100644
--- a/Doc/glossary.rst
+++ b/Doc/glossary.rst
@@ -243,7 +243,7 @@ Glossary
       Fortran contiguous arrays, the first index varies the fastest.
 
    coroutine
-      Coroutines is a more generalized form of subroutines. Subroutines are
+      Coroutines are a more generalized form of subroutines. Subroutines are
       entered at one point and exited at another point.  Coroutines can be
       entered, exited, and resumed at many different points.  They can be
       implemented with the :keyword:`async def` statement.  See also
diff --git a/Doc/library/asyncio-task.rst b/Doc/library/asyncio-task.rst
index a9f6f9cfc4b6260..9a4cda1887887c5 100644
--- a/Doc/library/asyncio-task.rst
+++ b/Doc/library/asyncio-task.rst
@@ -212,6 +212,8 @@ Running an asyncio Program
 
 .. function:: run(coro, \*, debug=False)
 
+    Execute the :term:`coroutine` *coro* and return the result.
+
     This function runs the passed coroutine, taking care of
     managing the asyncio event loop and *finalizing asynchronous
     generators*.
@@ -225,10 +227,6 @@ Running an asyncio Program
     the end.  It should be used as a main entry point for asyncio
     programs, and should ideally only be called once.
 
-    Return a result of *coro* execution, or raise a :exc:`RuntimeError`
-    if ``asyncio.run()`` is called from a running event loop, or a
-    :exc:`ValueError` if *coro* is not a courutine.
-
     Example::
 
         async def main():
diff --git a/Lib/asyncio/runners.py b/Lib/asyncio/runners.py
index df686386b8fd4ee..2e37e18b45fc150 100644
--- a/Lib/asyncio/runners.py
+++ b/Lib/asyncio/runners.py
@@ -6,7 +6,7 @@
 
 
 def run(main, *, debug=False):
-    """Run a coroutine.
+    """Execute the coroutine and return the result.
 
     This function runs the passed coroutine, taking care of
     managing the asyncio event loop and finalizing asynchronous
@@ -21,10 +21,6 @@ def run(main, *, debug=False):
     It should be used as a main entry point for asyncio programs, and should
     ideally only be called once.
 
-    Return a result of *coro* execution, or raise a RuntimeError
-    if `asyncio.run()`is called from a running event loop, or a ValueError
-    if `main` is not a courutine.
-
     Example:
 
         async def main():