diff --git a/doc/api/next_api_changes/removals.rst b/doc/api/next_api_changes/removals.rst
index 24da01c0e715..a8992ffab7c4 100644
--- a/doc/api/next_api_changes/removals.rst
+++ b/doc/api/next_api_changes/removals.rst
@@ -73,6 +73,14 @@ Classes and methods
 - ``scale.NaturalLogTransform`` (use ``scale.LogTransform`` instead)
 - ``scale.InvertedNaturalLogTransform`` (use ``scale.InvertedLogTransform`` instead)
 
+- ``spines.Spine.is_frame_like()`` (no replacement)
+
+- ``text.Text.is_math_text()`` (use ``cbook.is_math_text()`` instead)
+- ``text.TextWithDash()`` (use ``text.Annotation`` instead)
+- ``textpath.TextPath.is_math_text()`` (use ``cbook.is_math_text()`` instead)
+- ``textpath.TextPath.text_get_vertices_codes()``
+  (use ``textpath.text_to_path.get_text_path()`` instead)
+
 - ``ticker.OldScalarFormatter.pprint_val()`` (no replacement)
 - ``ticker.ScalarFormatter.pprint_val()`` (no replacement)
 - ``ticker.LogFormatter.pprint_val()`` (no replacement)
@@ -112,8 +120,6 @@ Classes and methods
 - ``path.get_paths_extents()``
   (use ``path.get_path_collection_extents()`` instead)
 
-- ``text.TextWithDash`` (use ``text.Annotation`` instead)
-
 - ``mplot3d.proj3d.line2d()`` (no replacement)
 - ``mplot3d.proj3d.line2d_dist()`` (no replacement)
 - ``mplot3d.proj3d.line2d_seg_dist()`` (no replacement)
@@ -142,6 +148,8 @@ Classes and methods
 - ``axisartist.axislines.Axes.AxisDict``
   (use ``axis_grid1.mpl_axes.Axes.AxisDict`` instead)
 
+- ``widgets.SpanSelector.buttonDown`` property (no replacement)
+
 Arguments
 ~~~~~~~~~
 - ``Axes.text()`` / ``pyplot.text()`` do not support the parameter ``withdash``
diff --git a/lib/matplotlib/spines.py b/lib/matplotlib/spines.py
index f364170bfe80..beb6be6e41e5 100644
--- a/lib/matplotlib/spines.py
+++ b/lib/matplotlib/spines.py
@@ -240,28 +240,6 @@ def cla(self):
         if self.axis is not None:
             self.axis.cla()
 
-    @cbook.deprecated("3.1")
-    def is_frame_like(self):
-        """Return True if directly on axes frame.
-
-        This is useful for determining if a spine is the edge of an
-        old style MPL plot. If so, this function will return True.
-        """
-        self._ensure_position_is_set()
-        position = self._position
-        if isinstance(position, str):
-            if position == 'center':
-                position = ('axes', 0.5)
-            elif position == 'zero':
-                position = ('data', 0)
-        if len(position) != 2:
-            raise ValueError("position should be 2-tuple")
-        position_type, amount = position
-        if position_type == 'outward' and amount == 0:
-            return True
-        else:
-            return False
-
     def _adjust_location(self):
         """Automatically set spine bounds to the view interval."""
 
diff --git a/lib/matplotlib/text.py b/lib/matplotlib/text.py
index f4e3fc8efcca..f1ff53f8d9f1 100644
--- a/lib/matplotlib/text.py
+++ b/lib/matplotlib/text.py
@@ -1174,30 +1174,6 @@ def set_text(self, s):
             self._text = str(s)
             self.stale = True
 
-    @staticmethod
-    @cbook.deprecated("3.1")
-    def is_math_text(s, usetex=None):
-        """
-        Returns a cleaned string and a boolean flag.
-        The flag indicates if the given string *s* contains any mathtext,
-        determined by counting unescaped dollar signs. If no mathtext
-        is present, the cleaned string has its dollar signs unescaped.
-        If usetex is on, the flag always has the value "TeX".
-        """
-        # Did we find an even number of non-escaped dollar signs?
-        # If so, treat is as math text.
-        if usetex is None:
-            usetex = rcParams['text.usetex']
-        if usetex:
-            if s == ' ':
-                s = r'\ '
-            return s, 'TeX'
-
-        if cbook.is_math_text(s):
-            return s, True
-        else:
-            return s.replace(r'\$', '$'), False
-
     def _preprocess_math(self, s):
         """
         Return the string *s* after mathtext preprocessing, and the kind of
diff --git a/lib/matplotlib/textpath.py b/lib/matplotlib/textpath.py
index 3c4b940624c1..1e0377007e1a 100644
--- a/lib/matplotlib/textpath.py
+++ b/lib/matplotlib/textpath.py
@@ -453,36 +453,3 @@ def _revalidate_path(self):
                   .translate(*self._xy))
             self._cached_vertices = tr.transform(self._vertices)
             self._invalid = False
-
-    @cbook.deprecated("3.1")
-    def is_math_text(self, s):
-        """
-        Returns True if the given string *s* contains any mathtext.
-        """
-        # copied from Text.is_math_text -JJL
-
-        # Did we find an even number of non-escaped dollar signs?
-        # If so, treat is as math text.
-        dollar_count = s.count(r'$') - s.count(r'\$')
-        even_dollars = (dollar_count > 0 and dollar_count % 2 == 0)
-
-        if rcParams['text.usetex']:
-            return s, 'TeX'
-
-        if even_dollars:
-            return s, True
-        else:
-            return s.replace(r'\$', '$'), False
-
-    @cbook.deprecated("3.1", alternative="TextPath")
-    def text_get_vertices_codes(self, prop, s, usetex):
-        """
-        Convert string *s* to a (vertices, codes) pair using font property
-        *prop*.
-        """
-        # Mostly copied from backend_svg.py.
-        if usetex:
-            return text_to_path.get_text_path(prop, s, usetex=True)
-        else:
-            clean_line, ismath = self.is_math_text(s)
-            return text_to_path.get_text_path(prop, clean_line, ismath=ismath)
diff --git a/lib/matplotlib/widgets.py b/lib/matplotlib/widgets.py
index 9259dc385541..3c664e11c6d4 100644
--- a/lib/matplotlib/widgets.py
+++ b/lib/matplotlib/widgets.py
@@ -1821,11 +1821,6 @@ def _release(self, event):
         self.pressv = None
         return False
 
-    @cbook.deprecated("3.1")
-    @property
-    def buttonDown(self):
-        return False
-
     def _onmove(self, event):
         """on motion notify event"""
         if self.pressv is None: