diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index eed48f9e46897..7af4795fbc3e8 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -60,7 +60,7 @@ Deprecations
 
 Removal of prior version deprecations/changes
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
+- Removed the previously deprecated :meth:`Series.get_value`, :meth:`Series.set_value`, :meth:`DataFrame.get_value`, :meth:`DataFrame.set_value` (:issue:`17739`)
 -
 -
 
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 4beaf301988b4..c5b7c958e1b5d 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -382,7 +382,7 @@ def _constructor(self):
 
     _constructor_sliced = Series  # type: Type[Series]
     _deprecations = NDFrame._deprecations | frozenset(
-        ["get_value", "set_value", "from_items"]
+        ["from_items"]
     )  # type: FrozenSet[str]
     _accessors = set()  # type: Set[str]
 
@@ -2779,13 +2779,10 @@ def _unpickle_matrix_compat(self, state):  # pragma: no cover
     # ----------------------------------------------------------------------
     # Getting and setting elements
 
-    def get_value(self, index, col, takeable=False):
+    def _get_value(self, index, col, takeable: bool = False):
         """
         Quickly retrieve single value at passed column and index.
 
-        .. deprecated:: 0.21.0
-            Use .at[] or .iat[] accessors instead.
-
         Parameters
         ----------
         index : row label
@@ -2796,18 +2793,6 @@ def get_value(self, index, col, takeable=False):
         -------
         scalar
         """
-
-        warnings.warn(
-            "get_value is deprecated and will be removed "
-            "in a future release. Please use "
-            ".at[] or .iat[] accessors instead",
-            FutureWarning,
-            stacklevel=2,
-        )
-        return self._get_value(index, col, takeable=takeable)
-
-    def _get_value(self, index, col, takeable=False):
-
         if takeable:
             series = self._iget_item_cache(col)
             return com.maybe_box_datetimelike(series._values[index])
@@ -2831,15 +2816,10 @@ def _get_value(self, index, col, takeable=False):
         index = self.index.get_loc(index)
         return self._get_value(index, col, takeable=True)
 
-    _get_value.__doc__ = get_value.__doc__
-
-    def set_value(self, index, col, value, takeable=False):
+    def _set_value(self, index, col, value, takeable: bool = False):
         """
         Put single value at passed column and index.
 
-        .. deprecated:: 0.21.0
-            Use .at[] or .iat[] accessors instead.
-
         Parameters
         ----------
         index : row label
@@ -2853,16 +2833,6 @@ def set_value(self, index, col, value, takeable=False):
             If label pair is contained, will be reference to calling DataFrame,
             otherwise a new object.
         """
-        warnings.warn(
-            "set_value is deprecated and will be removed "
-            "in a future release. Please use "
-            ".at[] or .iat[] accessors instead",
-            FutureWarning,
-            stacklevel=2,
-        )
-        return self._set_value(index, col, value, takeable=takeable)
-
-    def _set_value(self, index, col, value, takeable=False):
         try:
             if takeable is True:
                 series = self._iget_item_cache(col)
@@ -2883,8 +2853,6 @@ def _set_value(self, index, col, value, takeable=False):
 
             return self
 
-    _set_value.__doc__ = set_value.__doc__
-
     def _ixs(self, i: int, axis: int = 0):
         """
         Parameters
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 98a7b279f70b3..418b3fc8c57d0 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -179,7 +179,7 @@ class Series(base.IndexOpsMixin, generic.NDFrame):
     _accessors = {"dt", "cat", "str", "sparse"}
     # tolist is not actually deprecated, just suppressed in the __dir__
     _deprecations = generic.NDFrame._deprecations | frozenset(
-        ["asobject", "reshape", "get_value", "set_value", "valid", "tolist"]
+        ["asobject", "reshape", "valid", "tolist"]
     )
 
     # Override cache_readonly bc Series is mutable
@@ -1367,13 +1367,10 @@ def repeat(self, repeats, axis=None):
         new_values = self._values.repeat(repeats)
         return self._constructor(new_values, index=new_index).__finalize__(self)
 
-    def get_value(self, label, takeable=False):
+    def _get_value(self, label, takeable: bool = False):
         """
         Quickly retrieve single value at passed index label.
 
-        .. deprecated:: 0.21.0
-            Please use .at[] or .iat[] accessors.
-
         Parameters
         ----------
         label : object
@@ -1383,29 +1380,14 @@ def get_value(self, label, takeable=False):
         -------
         scalar value
         """
-        warnings.warn(
-            "get_value is deprecated and will be removed "
-            "in a future release. Please use "
-            ".at[] or .iat[] accessors instead",
-            FutureWarning,
-            stacklevel=2,
-        )
-        return self._get_value(label, takeable=takeable)
-
-    def _get_value(self, label, takeable=False):
-        if takeable is True:
+        if takeable:
             return com.maybe_box_datetimelike(self._values[label])
         return self.index.get_value(self._values, label)
 
-    _get_value.__doc__ = get_value.__doc__
-
-    def set_value(self, label, value, takeable=False):
+    def _set_value(self, label, value, takeable: bool = False):
         """
         Quickly set single value at passed label.
 
-        .. deprecated:: 0.21.0
-            Please use .at[] or .iat[] accessors.
-
         If label is not contained, a new object is created with the label
         placed at the end of the result index.
 
@@ -1423,16 +1405,6 @@ def set_value(self, label, value, takeable=False):
             If label is contained, will be reference to calling Series,
             otherwise a new object.
         """
-        warnings.warn(
-            "set_value is deprecated and will be removed "
-            "in a future release. Please use "
-            ".at[] or .iat[] accessors instead",
-            FutureWarning,
-            stacklevel=2,
-        )
-        return self._set_value(label, value, takeable=takeable)
-
-    def _set_value(self, label, value, takeable=False):
         try:
             if takeable:
                 self._values[label] = value
@@ -1445,8 +1417,6 @@ def _set_value(self, label, value, takeable=False):
 
         return self
 
-    _set_value.__doc__ = set_value.__doc__
-
     def reset_index(self, level=None, drop=False, name=None, inplace=False):
         """
         Generate a new DataFrame or Series with the index reset.
diff --git a/pandas/core/sparse/frame.py b/pandas/core/sparse/frame.py
index 54998eb66e69d..2dbf4807cf144 100644
--- a/pandas/core/sparse/frame.py
+++ b/pandas/core/sparse/frame.py
@@ -447,12 +447,10 @@ def sp_maker(x, index=None):
         # always return a SparseArray!
         return clean
 
-    def get_value(self, index, col, takeable=False):
+    def _get_value(self, index, col, takeable=False):
         """
         Quickly retrieve single value at passed column and index
 
-        .. deprecated:: 0.21.0
-
         Please use .at[] or .iat[] accessors.
 
         Parameters
@@ -465,16 +463,6 @@ def get_value(self, index, col, takeable=False):
         -------
         value : scalar value
         """
-        warnings.warn(
-            "get_value is deprecated and will be removed "
-            "in a future release. Please use "
-            ".at[] or .iat[] accessors instead",
-            FutureWarning,
-            stacklevel=2,
-        )
-        return self._get_value(index, col, takeable=takeable)
-
-    def _get_value(self, index, col, takeable=False):
         if takeable is True:
             series = self._iget_item_cache(col)
         else:
@@ -482,14 +470,10 @@ def _get_value(self, index, col, takeable=False):
 
         return series._get_value(index, takeable=takeable)
 
-    _get_value.__doc__ = get_value.__doc__
-
-    def set_value(self, index, col, value, takeable=False):
+    def _set_value(self, index, col, value, takeable=False):
         """
         Put single value at passed column and index
 
-        .. deprecated:: 0.21.0
-
         Please use .at[] or .iat[] accessors.
 
         Parameters
@@ -509,23 +493,11 @@ def set_value(self, index, col, value, takeable=False):
         -------
         frame : DataFrame
         """
-        warnings.warn(
-            "set_value is deprecated and will be removed "
-            "in a future release. Please use "
-            ".at[] or .iat[] accessors instead",
-            FutureWarning,
-            stacklevel=2,
-        )
-        return self._set_value(index, col, value, takeable=takeable)
-
-    def _set_value(self, index, col, value, takeable=False):
         dense = self.to_dense()._set_value(index, col, value, takeable=takeable)
         return dense.to_sparse(
             kind=self._default_kind, fill_value=self._default_fill_value
         )
 
-    _set_value.__doc__ = set_value.__doc__
-
     def _slice(self, slobj, axis=0, kind=None):
         if axis == 0:
             new_index = self.index[slobj]
diff --git a/pandas/core/sparse/series.py b/pandas/core/sparse/series.py
index 43f2609f46bd6..f5d39c47150a2 100644
--- a/pandas/core/sparse/series.py
+++ b/pandas/core/sparse/series.py
@@ -386,12 +386,10 @@ def get(self, label, default=None):
         else:
             return default
 
-    def get_value(self, label, takeable=False):
+    def _get_value(self, label, takeable=False):
         """
         Retrieve single value at passed index label
 
-        .. deprecated:: 0.21.0
-
         Please use .at[] or .iat[] accessors.
 
         Parameters
@@ -403,23 +401,10 @@ def get_value(self, label, takeable=False):
         -------
         value : scalar value
         """
-        warnings.warn(
-            "get_value is deprecated and will be removed "
-            "in a future release. Please use "
-            ".at[] or .iat[] accessors instead",
-            FutureWarning,
-            stacklevel=2,
-        )
-
-        return self._get_value(label, takeable=takeable)
-
-    def _get_value(self, label, takeable=False):
         loc = label if takeable is True else self.index.get_loc(label)
         return self._get_val_at(loc)
 
-    _get_value.__doc__ = get_value.__doc__
-
-    def set_value(self, label, value, takeable=False):
+    def _set_value(self, label, value, takeable=False):
         """
         Quickly set single value at passed label. If label is not contained, a
         new object is created with the label placed at the end of the result
@@ -446,16 +431,6 @@ def set_value(self, label, value, takeable=False):
         -------
         series : SparseSeries
         """
-        warnings.warn(
-            "set_value is deprecated and will be removed "
-            "in a future release. Please use "
-            ".at[] or .iat[] accessors instead",
-            FutureWarning,
-            stacklevel=2,
-        )
-        return self._set_value(label, value, takeable=takeable)
-
-    def _set_value(self, label, value, takeable=False):
         values = self.to_dense()
 
         # if the label doesn't exist, we will create a new object here
@@ -468,8 +443,6 @@ def _set_value(self, label, value, takeable=False):
         self._data = SingleBlockManager(values, new_index)
         self._index = new_index
 
-    _set_value.__doc__ = set_value.__doc__
-
     def _set_values(self, key, value):
 
         # this might be inefficient as we have to recreate the sparse array
diff --git a/pandas/tests/frame/test_api.py b/pandas/tests/frame/test_api.py
index b4b081cfe8d76..c6852576f660b 100644
--- a/pandas/tests/frame/test_api.py
+++ b/pandas/tests/frame/test_api.py
@@ -67,8 +67,7 @@ def test_getitem_pop_assign_name(self, float_frame):
     def test_get_value(self, float_frame):
         for idx in float_frame.index:
             for col in float_frame.columns:
-                with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-                    result = float_frame.get_value(idx, col)
+                result = float_frame._get_value(idx, col)
                 expected = float_frame[col][idx]
                 tm.assert_almost_equal(result, expected)
 
diff --git a/pandas/tests/frame/test_constructors.py b/pandas/tests/frame/test_constructors.py
index 29e46ac70c943..ebffeeaa3063e 100644
--- a/pandas/tests/frame/test_constructors.py
+++ b/pandas/tests/frame/test_constructors.py
@@ -329,10 +329,8 @@ def test_constructor_dict(self):
         # Dict with None value
         frame_none = DataFrame(dict(a=None), index=[0])
         frame_none_list = DataFrame(dict(a=[None]), index=[0])
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            assert frame_none.get_value(0, "a") is None
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            assert frame_none_list.get_value(0, "a") is None
+        assert frame_none._get_value(0, "a") is None
+        assert frame_none_list._get_value(0, "a") is None
         tm.assert_frame_equal(frame_none, frame_none_list)
 
         # GH10856
@@ -702,8 +700,7 @@ def test_nested_dict_frame_constructor(self):
         data = {}
         for col in df.columns:
             for row in df.index:
-                with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-                    data.setdefault(col, {})[row] = df.get_value(row, col)
+                data.setdefault(col, {})[row] = df._get_value(row, col)
 
         result = DataFrame(data, columns=rng)
         tm.assert_frame_equal(result, df)
@@ -711,8 +708,7 @@ def test_nested_dict_frame_constructor(self):
         data = {}
         for col in df.columns:
             for row in df.index:
-                with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-                    data.setdefault(row, {})[col] = df.get_value(row, col)
+                data.setdefault(row, {})[col] = df._get_value(row, col)
 
         result = DataFrame(data, index=rng).T
         tm.assert_frame_equal(result, df)
diff --git a/pandas/tests/frame/test_indexing.py b/pandas/tests/frame/test_indexing.py
index 0cb7db0e47123..0fb32dbfcd42d 100644
--- a/pandas/tests/frame/test_indexing.py
+++ b/pandas/tests/frame/test_indexing.py
@@ -1849,8 +1849,7 @@ def test_getitem_list_duplicates(self):
     def test_get_value(self, float_frame):
         for idx in float_frame.index:
             for col in float_frame.columns:
-                with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-                    result = float_frame.get_value(idx, col)
+                result = float_frame._get_value(idx, col)
                 expected = float_frame[col][idx]
                 assert result == expected
 
@@ -1905,42 +1904,34 @@ def test_lookup_raises(self, float_frame):
     def test_set_value(self, float_frame):
         for idx in float_frame.index:
             for col in float_frame.columns:
-                with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-                    float_frame.set_value(idx, col, 1)
+                float_frame._set_value(idx, col, 1)
                 assert float_frame[col][idx] == 1
 
     def test_set_value_resize(self, float_frame):
 
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            res = float_frame.set_value("foobar", "B", 0)
+        res = float_frame._set_value("foobar", "B", 0)
         assert res is float_frame
         assert res.index[-1] == "foobar"
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            assert res.get_value("foobar", "B") == 0
+        assert res._get_value("foobar", "B") == 0
 
         float_frame.loc["foobar", "qux"] = 0
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            assert float_frame.get_value("foobar", "qux") == 0
+        assert float_frame._get_value("foobar", "qux") == 0
 
         res = float_frame.copy()
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            res3 = res.set_value("foobar", "baz", "sam")
+        res3 = res._set_value("foobar", "baz", "sam")
         assert res3["baz"].dtype == np.object_
 
         res = float_frame.copy()
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            res3 = res.set_value("foobar", "baz", True)
+        res3 = res._set_value("foobar", "baz", True)
         assert res3["baz"].dtype == np.object_
 
         res = float_frame.copy()
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            res3 = res.set_value("foobar", "baz", 5)
+        res3 = res._set_value("foobar", "baz", 5)
         assert is_float_dtype(res3["baz"])
         assert isna(res3["baz"].drop(["foobar"])).all()
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            msg = "could not convert string to float: 'sam'"
-            with pytest.raises(ValueError, match=msg):
-                res3.set_value("foobar", "baz", "sam")
+        msg = "could not convert string to float: 'sam'"
+        with pytest.raises(ValueError, match=msg):
+            res3._set_value("foobar", "baz", "sam")
 
     def test_set_value_with_index_dtype_change(self):
         df_orig = DataFrame(np.random.randn(3, 3), index=range(3), columns=list("ABC"))
@@ -1948,8 +1939,7 @@ def test_set_value_with_index_dtype_change(self):
         # this is actually ambiguous as the 2 is interpreted as a positional
         # so column is not created
         df = df_orig.copy()
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            df.set_value("C", 2, 1.0)
+        df._set_value("C", 2, 1.0)
         assert list(df.index) == list(df_orig.index) + ["C"]
         # assert list(df.columns) == list(df_orig.columns) + [2]
 
@@ -1960,8 +1950,7 @@ def test_set_value_with_index_dtype_change(self):
 
         # create both new
         df = df_orig.copy()
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            df.set_value("C", "D", 1.0)
+        df._set_value("C", "D", 1.0)
         assert list(df.index) == list(df_orig.index) + ["C"]
         assert list(df.columns) == list(df_orig.columns) + ["D"]
 
@@ -1974,9 +1963,8 @@ def test_get_set_value_no_partial_indexing(self):
         # partial w/ MultiIndex raise exception
         index = MultiIndex.from_tuples([(0, 1), (0, 2), (1, 1), (1, 2)])
         df = DataFrame(index=index, columns=range(4))
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            with pytest.raises(KeyError, match=r"^0$"):
-                df.get_value(0, 1)
+        with pytest.raises(KeyError, match=r"^0$"):
+            df._get_value(0, 1)
 
     def test_single_element_ix_dont_upcast(self, float_frame):
         float_frame["E"] = 1
diff --git a/pandas/tests/series/indexing/test_datetime.py b/pandas/tests/series/indexing/test_datetime.py
index e0b84e8708fa1..bf8d34cd62ff2 100644
--- a/pandas/tests/series/indexing/test_datetime.py
+++ b/pandas/tests/series/indexing/test_datetime.py
@@ -110,17 +110,16 @@ def test_series_set_value():
     dates = [datetime(2001, 1, 1), datetime(2001, 1, 2)]
     index = DatetimeIndex(dates)
 
-    with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-        s = Series().set_value(dates[0], 1.0)
-    with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-        s2 = s.set_value(dates[1], np.nan)
+    s = Series()._set_value(dates[0], 1.0)
+    s2 = s._set_value(dates[1], np.nan)
 
-    exp = Series([1.0, np.nan], index=index)
+    expected = Series([1.0, np.nan], index=index)
 
-    assert_series_equal(s2, exp)
+    assert_series_equal(s2, expected)
 
+    # FIXME: dont leave commented-out
     # s = Series(index[:1], index[:1])
-    # s2 = s.set_value(dates[1], index[1])
+    # s2 = s._set_value(dates[1], index[1])
     # assert s2.values.dtype == 'M8[ns]'
 
 
diff --git a/pandas/tests/series/indexing/test_indexing.py b/pandas/tests/series/indexing/test_indexing.py
index 2d36bfdb93a17..f50b3ddbce7dc 100644
--- a/pandas/tests/series/indexing/test_indexing.py
+++ b/pandas/tests/series/indexing/test_indexing.py
@@ -372,15 +372,13 @@ def test_setitem_dtypes():
 
 def test_set_value(test_data):
     idx = test_data.ts.index[10]
-    with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-        res = test_data.ts.set_value(idx, 0)
+    res = test_data.ts._set_value(idx, 0)
     assert res is test_data.ts
     assert test_data.ts[idx] == 0
 
     # equiv
     s = test_data.series.copy()
-    with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-        res = s.set_value("foobar", 0)
+    res = s._set_value("foobar", 0)
     assert res is s
     assert res.index[-1] == "foobar"
     assert res["foobar"] == 0
diff --git a/pandas/tests/sparse/frame/test_frame.py b/pandas/tests/sparse/frame/test_frame.py
index 5682c74a8b692..ddb50e0897a86 100644
--- a/pandas/tests/sparse/frame/test_frame.py
+++ b/pandas/tests/sparse/frame/test_frame.py
@@ -538,28 +538,23 @@ def test_set_value(self, float_frame):
 
         # ok, as the index gets converted to object
         frame = float_frame.copy()
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            res = frame.set_value("foobar", "B", 1.5)
+        res = frame._set_value("foobar", "B", 1.5)
         assert res.index.dtype == "object"
 
         res = float_frame
         res.index = res.index.astype(object)
 
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            res = float_frame.set_value("foobar", "B", 1.5)
+        res = float_frame._set_value("foobar", "B", 1.5)
         assert res is not float_frame
         assert res.index[-1] == "foobar"
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            assert res.get_value("foobar", "B") == 1.5
+        assert res._get_value("foobar", "B") == 1.5
 
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            res2 = res.set_value("foobar", "qux", 1.5)
+        res2 = res._set_value("foobar", "qux", 1.5)
         assert res2 is not res
         tm.assert_index_equal(
             res2.columns, pd.Index(list(float_frame.columns) + ["qux"])
         )
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            assert res2.get_value("foobar", "qux") == 1.5
+        assert res2._get_value("foobar", "qux") == 1.5
 
     def test_fancy_index_misc(self, float_frame):
         # axis = 0
diff --git a/pandas/tests/sparse/series/test_series.py b/pandas/tests/sparse/series/test_series.py
index a9c3d157dd69b..046e7745fd4ec 100644
--- a/pandas/tests/sparse/series/test_series.py
+++ b/pandas/tests/sparse/series/test_series.py
@@ -470,18 +470,15 @@ def test_get_get_value(self):
         expected = self.btseries.to_dense()[dt]
         tm.assert_almost_equal(result, expected)
 
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            tm.assert_almost_equal(self.bseries.get_value(10), self.bseries[10])
+        tm.assert_almost_equal(self.bseries._get_value(10), self.bseries[10])
 
     def test_set_value(self):
 
         idx = self.btseries.index[7]
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            self.btseries.set_value(idx, 0)
+        self.btseries._set_value(idx, 0)
         assert self.btseries[idx] == 0
 
-        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
-            self.iseries.set_value("foobar", 0)
+        self.iseries._set_value("foobar", 0)
         assert self.iseries.index[-1] == "foobar"
         assert self.iseries["foobar"] == 0