diff --git a/doc/source/whatsnew/v0.22.0.txt b/doc/source/whatsnew/v0.22.0.txt
index 0579a80aad28e..fcca50d1acdfd 100644
--- a/doc/source/whatsnew/v0.22.0.txt
+++ b/doc/source/whatsnew/v0.22.0.txt
@@ -139,6 +139,8 @@ Other Enhancements
 - :func:`read_excel()` has gained the ``nrows`` parameter (:issue:`16645`)
 - :func:``DataFrame.to_json`` and ``Series.to_json`` now accept an ``index`` argument which allows the user to exclude the index from the JSON output (:issue:`17394`)
 - ``IntervalIndex.to_tuples()`` has gained the ``na_tuple`` parameter to control whether NA is returned as a tuple of NA, or NA itself (:issue:`18756`)
+- ``Categorical.rename_categories``, ``CategoricalIndex.rename_categories`` and :attr:`Series.cat.rename_categories`
+  can now take a callable as their argument (:issue:`18862`)
 
 .. _whatsnew_0220.api_breaking:
 
diff --git a/pandas/core/categorical.py b/pandas/core/categorical.py
index 356e76df366b4..f9bd6849c5072 100644
--- a/pandas/core/categorical.py
+++ b/pandas/core/categorical.py
@@ -844,7 +844,7 @@ def rename_categories(self, new_categories, inplace=False):
 
         Parameters
         ----------
-        new_categories : list-like or dict-like
+        new_categories : list-like, dict-like or callable
 
            * list-like: all items must be unique and the number of items in
              the new categories must match the existing number of categories.
@@ -852,7 +852,14 @@ def rename_categories(self, new_categories, inplace=False):
            * dict-like: specifies a mapping from
              old categories to new. Categories not contained in the mapping
              are passed through and extra categories in the mapping are
-             ignored. *New in version 0.21.0*.
+             ignored.
+
+             .. versionadded:: 0.21.0
+
+           * callable : a callable that is called on all items in the old
+             categories and whose return values comprise the new categories.
+
+             .. versionadded:: 0.22.0
 
            .. warning::
 
@@ -890,6 +897,12 @@ def rename_categories(self, new_categories, inplace=False):
         >>> c.rename_categories({'a': 'A', 'c': 'C'})
         [A, A, b]
         Categories (2, object): [A, b]
+
+        You may also provide a callable to create the new categories
+
+        >>> c.rename_categories(lambda x: x.upper())
+        [A, A, B]
+        Categories (2, object): [A, B]
         """
         inplace = validate_bool_kwarg(inplace, 'inplace')
         cat = self if inplace else self.copy()
@@ -906,6 +919,8 @@ def rename_categories(self, new_categories, inplace=False):
         if is_dict_like(new_categories):
             cat.categories = [new_categories.get(item, item)
                               for item in cat.categories]
+        elif callable(new_categories):
+            cat.categories = [new_categories(item) for item in cat.categories]
         else:
             cat.categories = new_categories
         if not inplace:
diff --git a/pandas/tests/categorical/test_api.py b/pandas/tests/categorical/test_api.py
index 7cc0aafaf05b6..12db4a9bea28b 100644
--- a/pandas/tests/categorical/test_api.py
+++ b/pandas/tests/categorical/test_api.py
@@ -71,9 +71,14 @@ def test_rename_categories(self):
 
         exp_cat = Index(["a", "b", "c"])
         tm.assert_index_equal(cat.categories, exp_cat)
-        res = cat.rename_categories([1, 2, 3], inplace=True)
+
+        # GH18862 (let rename_categories take callables)
+        result = cat.rename_categories(lambda x: x.upper())
+        expected = Categorical(["A", "B", "C", "A"])
+        tm.assert_categorical_equal(result, expected)
 
         # and now inplace
+        res = cat.rename_categories([1, 2, 3], inplace=True)
         assert res is None
         tm.assert_numpy_array_equal(cat.__array__(), np.array([1, 2, 3, 1],
                                                               dtype=np.int64))
diff --git a/pandas/tests/indexes/test_category.py b/pandas/tests/indexes/test_category.py
index 543f59013ff12..f7328a99195b9 100644
--- a/pandas/tests/indexes/test_category.py
+++ b/pandas/tests/indexes/test_category.py
@@ -185,6 +185,11 @@ def test_method_delegation(self):
         tm.assert_index_equal(result, CategoricalIndex(
             list('ffggef'), categories=list('efg')))
 
+        # GH18862 (let rename_categories take callables)
+        result = ci.rename_categories(lambda x: x.upper())
+        tm.assert_index_equal(result, CategoricalIndex(
+            list('AABBCA'), categories=list('CAB')))
+
         ci = CategoricalIndex(list('aabbca'), categories=list('cab'))
         result = ci.add_categories(['d'])
         tm.assert_index_equal(result, CategoricalIndex(
diff --git a/pandas/tests/series/test_api.py b/pandas/tests/series/test_api.py
index 617ca2199f588..a2838f803421c 100644
--- a/pandas/tests/series/test_api.py
+++ b/pandas/tests/series/test_api.py
@@ -588,6 +588,14 @@ def f():
         pytest.raises(Exception, f)
         # right: s.cat.set_categories([4,3,2,1])
 
+        # GH18862 (let Series.cat.rename_categories take callables)
+        s = Series(Categorical(["a", "b", "c", "a"], ordered=True))
+        result = s.cat.rename_categories(lambda x: x.upper())
+        expected = Series(Categorical(["A", "B", "C", "A"],
+                                      categories=["A", "B", "C"],
+                                      ordered=True))
+        tm.assert_series_equal(result, expected)
+
     def test_str_accessor_api_for_categorical(self):
         # https://github.com/pandas-dev/pandas/issues/10661
         from pandas.core.strings import StringMethods