diff --git a/doc/source/whatsnew/v1.0.2.rst b/doc/source/whatsnew/v1.0.2.rst
index 0c012e5c1417b..805f87b63eef8 100644
--- a/doc/source/whatsnew/v1.0.2.rst
+++ b/doc/source/whatsnew/v1.0.2.rst
@@ -29,6 +29,7 @@ Bug fixes
 **Categorical**
 
 - Fixed bug where :meth:`Categorical.from_codes` improperly raised a ``ValueError`` when passed nullable integer codes. (:issue:`31779`)
+- Bug in :class:`Categorical` that would ignore or crash when calling :meth:`Series.replace` with a list-like ``to_replace`` (:issue:`31720`)
 
 **I/O**
 
diff --git a/pandas/_testing.py b/pandas/_testing.py
index 1fdc5d478aaf6..ca378e5ce8f77 100644
--- a/pandas/_testing.py
+++ b/pandas/_testing.py
@@ -1056,6 +1056,7 @@ def assert_series_equal(
     check_exact=False,
     check_datetimelike_compat=False,
     check_categorical=True,
+    check_category_order=True,
     obj="Series",
 ):
     """
@@ -1090,6 +1091,10 @@ def assert_series_equal(
         Compare datetime-like which is comparable ignoring dtype.
     check_categorical : bool, default True
         Whether to compare internal Categorical exactly.
+    check_category_order : bool, default True
+        Whether to compare category order of internal Categoricals
+
+        .. versionadded:: 1.0.2
     obj : str, default 'Series'
         Specify object name being compared, internally used to show appropriate
         assertion message.
@@ -1192,7 +1197,12 @@ def assert_series_equal(
 
     if check_categorical:
         if is_categorical_dtype(left) or is_categorical_dtype(right):
-            assert_categorical_equal(left.values, right.values, obj=f"{obj} category")
+            assert_categorical_equal(
+                left.values,
+                right.values,
+                obj=f"{obj} category",
+                check_category_order=check_category_order,
+            )
 
 
 # This could be refactored to use the NDFrame.equals method
diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 52d9df0c2d508..d8a2fbdd58382 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -2447,18 +2447,30 @@ def replace(self, to_replace, value, inplace: bool = False):
         """
         inplace = validate_bool_kwarg(inplace, "inplace")
         cat = self if inplace else self.copy()
-        if to_replace in cat.categories:
-            if isna(value):
-                cat.remove_categories(to_replace, inplace=True)
-            else:
+
+        # build a dict of (to replace -> value) pairs
+        if is_list_like(to_replace):
+            # if to_replace is list-like and value is scalar
+            replace_dict = {replace_value: value for replace_value in to_replace}
+        else:
+            # if both to_replace and value are scalar
+            replace_dict = {to_replace: value}
+
+        # other cases, like if both to_replace and value are list-like or if
+        # to_replace is a dict, are handled separately in NDFrame
+        for replace_value, new_value in replace_dict.items():
+            if replace_value in cat.categories:
+                if isna(new_value):
+                    cat.remove_categories(replace_value, inplace=True)
+                    continue
                 categories = cat.categories.tolist()
-                index = categories.index(to_replace)
-                if value in cat.categories:
-                    value_index = categories.index(value)
+                index = categories.index(replace_value)
+                if new_value in cat.categories:
+                    value_index = categories.index(new_value)
                     cat._codes[cat._codes == index] = value_index
-                    cat.remove_categories(to_replace, inplace=True)
+                    cat.remove_categories(replace_value, inplace=True)
                 else:
-                    categories[index] = value
+                    categories[index] = new_value
                     cat.rename_categories(categories, inplace=True)
         if not inplace:
             return cat
diff --git a/pandas/tests/arrays/categorical/test_replace.py b/pandas/tests/arrays/categorical/test_replace.py
new file mode 100644
index 0000000000000..52530123bd52f
--- /dev/null
+++ b/pandas/tests/arrays/categorical/test_replace.py
@@ -0,0 +1,48 @@
+import pytest
+
+import pandas as pd
+import pandas._testing as tm
+
+
+@pytest.mark.parametrize(
+    "to_replace,value,expected,check_types,check_categorical",
+    [
+        # one-to-one
+        (1, 2, [2, 2, 3], True, True),
+        (1, 4, [4, 2, 3], True, True),
+        (4, 1, [1, 2, 3], True, True),
+        (5, 6, [1, 2, 3], True, True),
+        # many-to-one
+        ([1], 2, [2, 2, 3], True, True),
+        ([1, 2], 3, [3, 3, 3], True, True),
+        ([1, 2], 4, [4, 4, 3], True, True),
+        ((1, 2, 4), 5, [5, 5, 3], True, True),
+        ((5, 6), 2, [1, 2, 3], True, True),
+        # many-to-many, handled outside of Categorical and results in separate dtype
+        ([1], [2], [2, 2, 3], False, False),
+        ([1, 4], [5, 2], [5, 2, 3], False, False),
+        # check_categorical sorts categories, which crashes on mixed dtypes
+        (3, "4", [1, 2, "4"], True, False),
+        ([1, 2, "3"], "5", ["5", "5", 3], True, False),
+    ],
+)
+def test_replace(to_replace, value, expected, check_types, check_categorical):
+    # GH 31720
+    s = pd.Series([1, 2, 3], dtype="category")
+    result = s.replace(to_replace, value)
+    expected = pd.Series(expected, dtype="category")
+    s.replace(to_replace, value, inplace=True)
+    tm.assert_series_equal(
+        expected,
+        result,
+        check_dtype=check_types,
+        check_categorical=check_categorical,
+        check_category_order=False,
+    )
+    tm.assert_series_equal(
+        expected,
+        s,
+        check_dtype=check_types,
+        check_categorical=check_categorical,
+        check_category_order=False,
+    )