diff --git a/Doc/c-api/mapping.rst b/Doc/c-api/mapping.rst
index 308a976..b8eaadb 100644
--- a/Doc/c-api/mapping.rst
+++ b/Doc/c-api/mapping.rst
@@ -5,11 +5,17 @@
 Mapping Protocol
 ================
 
+See also :c:func:`PyObject_GetItem`, :c:func:`PyObject_SetItem` and
+:c:func:`PyObject_DelItem`.
+
 
 .. c:function:: int PyMapping_Check(PyObject *o)
 
-   Return ``1`` if the object provides mapping protocol, and ``0`` otherwise.  This
-   function always succeeds.
+   Return ``1`` if the object provides mapping protocol or supports slicing,
+   and ``0`` otherwise.  Note that it returns ``1`` for Python classes with
+   a :meth:`__getitem__` method since in general case it is impossible to
+   determine what the type of keys it supports.  This function always
+   succeeds.
 
 
 .. c:function:: Py_ssize_t PyMapping_Size(PyObject *o)
@@ -17,35 +23,49 @@
 
    .. index:: builtin: len
 
-   Returns the number of keys in object *o* on success, and ``-1`` on failure.  For
-   objects that do not provide mapping protocol, this is equivalent to the Python
-   expression ``len(o)``.
+   Returns the number of keys in object *o* on success, and ``-1`` on failure.
+   This is equivalent to the Python expression ``len(o)``.
 
 
-.. c:function:: int PyMapping_DelItemString(PyObject *o, const char *key)
+.. c:function:: PyObject* PyMapping_GetItemString(PyObject *o, const char *key)
 
-   Remove the mapping for object *key* from the object *o*. Return ``-1`` on
-   failure.  This is equivalent to the Python statement ``del o[key]``.
+   Return element of *o* corresponding to the string *key* or *NULL* on failure.
+   This is the equivalent of the Python expression ``o[key]``.
+   See also :c:func:`PyObject_GetItem`.
+
+
+.. c:function:: int PyMapping_SetItemString(PyObject *o, const char *key, PyObject *v)
+
+   Map the string *key* to the value *v* in object *o*.  Returns ``-1`` on
+   failure.  This is the equivalent of the Python statement ``o[key] = v``.
+   See also :c:func:`PyObject_SetItem`.
 
 
 .. c:function:: int PyMapping_DelItem(PyObject *o, PyObject *key)
 
-   Remove the mapping for object *key* from the object *o*. Return ``-1`` on
-   failure.  This is equivalent to the Python statement ``del o[key]``.
+   Remove the mapping for the object *key* from the object *o*.  Return ``-1``
+   on failure.  This is equivalent to the Python statement ``del o[key]``.
+   This is an alias of :c:func:`PyObject_DelItem`.
 
 
-.. c:function:: int PyMapping_HasKeyString(PyObject *o, const char *key)
+.. c:function:: int PyMapping_DelItemString(PyObject *o, const char *key)
 
-   On success, return ``1`` if the mapping object has the key *key* and ``0``
-   otherwise.  This is equivalent to the Python expression ``key in o``.
-   This function always succeeds.
+   Remove the mapping for the string *key* from the object *o*.  Return ``-1``
+   on failure.  This is equivalent to the Python statement ``del o[key]``.
 
 
 .. c:function:: int PyMapping_HasKey(PyObject *o, PyObject *key)
 
-   Return ``1`` if the mapping object has the key *key* and ``0`` otherwise.  This
-   is equivalent to the Python expression ``key in o``.  This function always
-   succeeds.
+   Return ``1`` if the mapping object has the key *key* and ``0`` otherwise.
+   This is equivalent to the Python expression ``key in o``.
+   This function always succeeds.
+
+
+.. c:function:: int PyMapping_HasKeyString(PyObject *o, const char *key)
+
+   Return ``1`` if the mapping object has the key *key* and ``0`` otherwise.
+   This is equivalent to the Python expression ``key in o``.
+   This function always succeeds.
 
 
 .. c:function:: PyObject* PyMapping_Keys(PyObject *o)
@@ -73,15 +93,3 @@
 
    .. versionchanged:: 3.7
       Previously, the function returned a list or a tuple.
-
-
-.. c:function:: PyObject* PyMapping_GetItemString(PyObject *o, const char *key)
-
-   Return element of *o* corresponding to the object *key* or *NULL* on failure.
-   This is the equivalent of the Python expression ``o[key]``.
-
-
-.. c:function:: int PyMapping_SetItemString(PyObject *o, const char *key, PyObject *v)
-
-   Map the object *key* to the value *v* in object *o*. Returns ``-1`` on failure.
-   This is the equivalent of the Python statement ``o[key] = v``.
diff --git a/Doc/c-api/object.rst b/Doc/c-api/object.rst
index 754dedc..f0b2005 100644
--- a/Doc/c-api/object.rst
+++ b/Doc/c-api/object.rst
@@ -379,8 +379,8 @@
    parameters must be non-*NULL*.
 
 
-.. c:function:: Py_ssize_t PyObject_Length(PyObject *o)
-               Py_ssize_t PyObject_Size(PyObject *o)
+.. c:function:: Py_ssize_t PyObject_Size(PyObject *o)
+               Py_ssize_t PyObject_Length(PyObject *o)
 
    .. index:: builtin: len
 
@@ -414,8 +414,8 @@
 
 .. c:function:: int PyObject_DelItem(PyObject *o, PyObject *key)
 
-   Delete the mapping for *key* from *o*.  Returns ``-1`` on failure. This is the
-   equivalent of the Python statement ``del o[key]``.
+   Remove the mapping for the object *key* from the object *o*.  Return ``-1``
+   on failure.  This is equivalent to the Python statement ``del o[key]``.
 
 
 .. c:function:: PyObject* PyObject_Dir(PyObject *o)
diff --git a/Doc/c-api/sequence.rst b/Doc/c-api/sequence.rst
index 81f8557..6d22f35 100644
--- a/Doc/c-api/sequence.rst
+++ b/Doc/c-api/sequence.rst
@@ -9,7 +9,10 @@
 .. c:function:: int PySequence_Check(PyObject *o)
 
    Return ``1`` if the object provides sequence protocol, and ``0`` otherwise.
-   This function always succeeds.
+   Note that it returns ``1`` for Python classes with a :meth:`__getitem__`
+   method unless they are :class:`dict` subclasses since in general case it
+   is impossible to determine what the type of keys it supports.  This
+   function always succeeds.
 
 
 .. c:function:: Py_ssize_t PySequence_Size(PyObject *o)
@@ -119,18 +122,27 @@
 
    .. index:: builtin: tuple
 
-   Return a tuple object with the same contents as the arbitrary sequence *o* or
-   *NULL* on failure.  If *o* is a tuple, a new reference will be returned,
+   Return a tuple object with the same contents as the sequence or iterable *o*,
+   or *NULL* on failure.  If *o* is a tuple, a new reference will be returned,
    otherwise a tuple will be constructed with the appropriate contents.  This is
    equivalent to the Python expression ``tuple(o)``.
 
 
 .. c:function:: PyObject* PySequence_Fast(PyObject *o, const char *m)
 
-   Return the sequence *o* as a list, unless it is already a tuple or list, in
+   Return the sequence or iterable *o* as a list, unless it is already a tuple or list, in
    which case *o* is returned.  Use :c:func:`PySequence_Fast_GET_ITEM` to access
    the members of the result.  Returns *NULL* on failure.  If the object is not
-   a sequence, raises :exc:`TypeError` with *m* as the message text.
+   a sequence or iterable, raises :exc:`TypeError` with *m* as the message text.
+
+
+.. c:function:: Py_ssize_t PySequence_Fast_GET_SIZE(PyObject *o)
+
+   Returns the length of *o*, assuming that *o* was returned by
+   :c:func:`PySequence_Fast` and that *o* is not *NULL*.  The size can also be
+   gotten by calling :c:func:`PySequence_Size` on *o*, but
+   :c:func:`PySequence_Fast_GET_SIZE` is faster because it can assume *o* is a list
+   or tuple.
 
 
 .. c:function:: PyObject* PySequence_Fast_GET_ITEM(PyObject *o, Py_ssize_t i)
@@ -155,12 +167,3 @@
    :c:func:`PySequence_GetItem` but without checking that
    :c:func:`PySequence_Check` on *o* is true and without adjustment for negative
    indices.
-
-
-.. c:function:: Py_ssize_t PySequence_Fast_GET_SIZE(PyObject *o)
-
-   Returns the length of *o*, assuming that *o* was returned by
-   :c:func:`PySequence_Fast` and that *o* is not *NULL*.  The size can also be
-   gotten by calling :c:func:`PySequence_Size` on *o*, but
-   :c:func:`PySequence_Fast_GET_SIZE` is faster because it can assume *o* is a list
-   or tuple.
diff --git a/Doc/c-api/typeobj.rst b/Doc/c-api/typeobj.rst
index 3bdf45a..6cbcc27 100644
--- a/Doc/c-api/typeobj.rst
+++ b/Doc/c-api/typeobj.rst
@@ -1167,21 +1167,24 @@
 
 .. c:member:: lenfunc PyMappingMethods.mp_length
 
-   This function is used by :c:func:`PyMapping_Length` and
+   This function is used by :c:func:`PyMapping_Size` and
    :c:func:`PyObject_Size`, and has the same signature.  This slot may be set to
    *NULL* if the object has no defined length.
 
 .. c:member:: binaryfunc PyMappingMethods.mp_subscript
 
-   This function is used by :c:func:`PyObject_GetItem` and has the same
-   signature.  This slot must be filled for the :c:func:`PyMapping_Check`
-   function to return ``1``, it can be *NULL* otherwise.
+   This function is used by :c:func:`PyObject_GetItem` and
+   :c:func:`PySequence_GetSlice`, and has the same signature as
+   :c:func:`!PyObject_GetItem`.  This slot must be filled for the
+   :c:func:`PyMapping_Check` function to return ``1``, it can be *NULL*
+   otherwise.
 
 .. c:member:: objobjargproc PyMappingMethods.mp_ass_subscript
 
-   This function is used by :c:func:`PyObject_SetItem` and
-   :c:func:`PyObject_DelItem`.  It has the same signature as
-   :c:func:`PyObject_SetItem`, but *v* can also be set to *NULL* to delete
+   This function is used by :c:func:`PyObject_SetItem`,
+   :c:func:`PyObject_DelItem`, :c:func:`PyObject_SetSlice` and
+   :c:func:`PyObject_DelSlice`.  It has the same signature as
+   :c:func:`!PyObject_SetItem`, but *v* can also be set to *NULL* to delete
    an item.  If this slot is *NULL*, the object does not support item
    assignment and deletion.
 
@@ -1201,26 +1204,29 @@
 
 .. c:member:: lenfunc PySequenceMethods.sq_length
 
-   This function is used by :c:func:`PySequence_Size` and :c:func:`PyObject_Size`,
-   and has the same signature.
+   This function is used by :c:func:`PySequence_Size` and
+   :c:func:`PyObject_Size`, and has the same signature.  It is also used for
+   handling negative indices via the :c:member:`~PySequenceMethods.sq_item`
+   and the :c:member:`~PySequenceMethods.sq_ass_item` slots.
 
 .. c:member:: binaryfunc PySequenceMethods.sq_concat
 
    This function is used by :c:func:`PySequence_Concat` and has the same
    signature.  It is also used by the ``+`` operator, after trying the numeric
-   addition via the :c:member:`~PyTypeObject.tp_as_number.nb_add` slot.
+   addition via the :c:member:`~PyNumberMethods.nb_add` slot.
 
 .. c:member:: ssizeargfunc PySequenceMethods.sq_repeat
 
    This function is used by :c:func:`PySequence_Repeat` and has the same
    signature.  It is also used by the ``*`` operator, after trying numeric
-   multiplication via the :c:member:`~PyTypeObject.tp_as_number.nb_multiply`
-   slot.
+   multiplication via the :c:member:`~PyNumberMethods.nb_multiply` slot.
 
 .. c:member:: ssizeargfunc PySequenceMethods.sq_item
 
    This function is used by :c:func:`PySequence_GetItem` and has the same
-   signature.  This slot must be filled for the :c:func:`PySequence_Check`
+   signature.  It is also used by :c:func:`PyObject_GetItem`, after trying
+   the subscription via the :c:member:`~PyMappingMethods.mp_subscript` slot.
+   This slot must be filled for the :c:func:`PySequence_Check`
    function to return ``1``, it can be *NULL* otherwise.
 
    Negative indexes are handled as follows: if the :attr:`sq_length` slot is
@@ -1231,28 +1237,36 @@
 .. c:member:: ssizeobjargproc PySequenceMethods.sq_ass_item
 
    This function is used by :c:func:`PySequence_SetItem` and has the same
-   signature.  This slot may be left to *NULL* if the object does not support
+   signature.  It is also used by :c:func:`PyObject_SetItem` and
+   :c:func:`PyObject_DelItem`, after trying the item assignment and deletion
+   via the :c:member:`~PyMappingMethods.mp_ass_subscript` slot.
+   This slot may be left to *NULL* if the object does not support
    item assignment and deletion.
 
 .. c:member:: objobjproc PySequenceMethods.sq_contains
 
    This function may be used by :c:func:`PySequence_Contains` and has the same
    signature.  This slot may be left to *NULL*, in this case
-   :c:func:`PySequence_Contains` simply traverses the sequence until it finds a
-   match.
+   :c:func:`!PySequence_Contains` simply traverses the sequence until it
+   finds a match.
 
 .. c:member:: binaryfunc PySequenceMethods.sq_inplace_concat
 
    This function is used by :c:func:`PySequence_InPlaceConcat` and has the same
-   signature.  It should modify its first operand, and return it.
+   signature.  It should modify its first operand, and return it.  This slot
+   may be left to *NULL*, in this case :c:func:`!PySequence_InPlaceConcat`
+   will fall back to :c:func:`PySequence_Concat`.  It is also used by the
+   augmented assignment ``+=``, after trying numeric inplace addition
+   via the :c:member:`~PyNumberMethods.nb_inplace_add` slot.
 
 .. c:member:: ssizeargfunc PySequenceMethods.sq_inplace_repeat
 
    This function is used by :c:func:`PySequence_InPlaceRepeat` and has the same
-   signature.  It should modify its first operand, and return it.
-
-.. XXX need to explain precedence between mapping and sequence
-.. XXX explains when to implement the sq_inplace_* slots
+   signature.  It should modify its first operand, and return it.  This slot
+   may be left to *NULL*, in this case :c:func:`!PySequence_InPlaceRepeat`
+   will fall back to :c:func:`PySequence_Repeat`.  It is also used by the
+   augmented assignment ``*=``, after trying numeric inplace multiplication
+   via the :c:member:`~PyNumberMethods.nb_inplace_multiply` slot.
 
 
 .. _buffer-structs:
diff --git a/Include/abstract.h b/Include/abstract.h
index 3133cd1..4088f75 100644
--- a/Include/abstract.h
+++ b/Include/abstract.h
@@ -442,13 +442,14 @@
    This is the equivalent of the Python statement: o[key]=v. */
 PyAPI_FUNC(int) PyObject_SetItem(PyObject *o, PyObject *key, PyObject *v);
 
-/* Remove the mapping for object, key, from the object 'o'.
+/* Remove the mapping for the string 'key' from the object 'o'.
    Returns -1 on failure.
 
    This is equivalent to the Python statement: del o[key]. */
 PyAPI_FUNC(int) PyObject_DelItemString(PyObject *o, const char *key);
 
-/* Delete the mapping for key from object 'o'. Returns -1 on failure.
+/* Delete the mapping for the object 'key' from the object 'o'.
+   Returns -1 on failure.
 
    This is the equivalent of the Python statement: del o[key]. */
 PyAPI_FUNC(int) PyObject_DelItem(PyObject *o, PyObject *key);
@@ -1005,8 +1006,7 @@
 PyAPI_FUNC(int) PyMapping_Check(PyObject *o);
 
 /* Returns the number of keys in mapping object 'o' on success, and -1 on
-  failure. For objects that do not provide sequence protocol, this is
-  equivalent to the Python expression: len(o). */
+  failure. This is equivalent to the Python expression: len(o). */
 PyAPI_FUNC(Py_ssize_t) PyMapping_Size(PyObject *o);
 
 /* For DLL compatibility */
@@ -1019,7 +1019,7 @@
 
    int PyMapping_DelItemString(PyObject *o, const char *key);
 
-   Remove the mapping for object 'key' from the mapping 'o'. Returns -1 on
+   Remove the mapping for the string 'key' from the mapping 'o'. Returns -1 on
    failure.
 
    This is equivalent to the Python statement: del o[key]. */
@@ -1029,7 +1029,7 @@
 
    int PyMapping_DelItem(PyObject *o, PyObject *key);
 
-   Remove the mapping for object 'key' from the mapping object 'o'.
+   Remove the mapping for the object 'key' from the mapping object 'o'.
    Returns -1 on failure.
 
    This is equivalent to the Python statement: del o[key]. */
@@ -1063,13 +1063,13 @@
    NULL. */
 PyAPI_FUNC(PyObject *) PyMapping_Items(PyObject *o);
 
-/* Return element of o corresponding to the object, key, or NULL on failure.
+/* Return element of 'o' corresponding to the string 'key' or NULL on failure.
 
    This is the equivalent of the Python expression: o[key]. */
 PyAPI_FUNC(PyObject *) PyMapping_GetItemString(PyObject *o,
                                                const char *key);
 
-/* Map the object 'key' to the value 'v' in the mapping 'o'.
+/* Map the string 'key' to the value 'v' in the mapping 'o'.
    Returns -1 on failure.
 
    This is the equivalent of the Python statement: o[key]=v. */