diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index 2b68ddf3d8918..5ec56018d7107 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -407,6 +407,9 @@ or ``matplotlib.Axes.plot``. See :ref:`plotting.formatters` for more.
 - Removed the previously deprecated :meth:`DataFrame.get_ftype_counts`, :meth:`Series.get_ftype_counts` (:issue:`18243`)
 - Removed the previously deprecated :meth:`Index.get_duplicated`, use ``idx[idx.duplicated()].unique()`` instead (:issue:`20239`)
 - Removed the previously deprecated :meth:`Series.clip_upper`, :meth:`Series.clip_lower`, :meth:`DataFrame.clip_upper`, :meth:`DataFrame.clip_lower` (:issue:`24203`)
+- Removed the ability to alter :attr:`DatetimeIndex.freq`, :attr:`TimedeltaIndex.freq`, or :attr:`PeriodIndex.freq` (:issue:`20772`)
+- Removed the previously deprecated :attr:`DatetimeIndex.offset` (:issue:`20730`)
+- Removed the previously deprecated :meth:`DatetimeIndex.asobject`, :meth:`TimedeltaIndex.asobject`, :meth:`PeriodIndex.asobject`, use ``astype(object)`` instead (:issue:`29801`)
 - Removed previously deprecated "order" argument from :func:`factorize` (:issue:`19751`)
 - Removed previously deprecated "v" argument from :meth:`FrozenNDarray.searchsorted`, use "value" instead (:issue:`22672`)
 - :func:`read_stata` and :meth:`DataFrame.to_stata` no longer supports the "encoding" argument (:issue:`21400`)
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index e420cf0cb0d78..b41227871ae03 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -3,7 +3,6 @@
 """
 import operator
 from typing import Set
-import warnings
 
 import numpy as np
 
@@ -104,11 +103,6 @@ def freq(self):
         """
         return self._data.freq
 
-    @freq.setter
-    def freq(self, value):
-        # validation is handled by _data setter
-        self._data.freq = value
-
     @property
     def freqstr(self):
         """
@@ -332,23 +326,6 @@ def take(self, indices, axis=0, allow_fill=True, fill_value=None, **kwargs):
     _na_value = NaT
     """The expected NA value to use with this index."""
 
-    @property
-    def asobject(self):
-        """
-        Return object Index which contains boxed values.
-
-        .. deprecated:: 0.23.0
-            Use ``astype(object)`` instead.
-
-        *this is an internal non-public method*
-        """
-        warnings.warn(
-            "'asobject' is deprecated. Use 'astype(object)' instead",
-            FutureWarning,
-            stacklevel=2,
-        )
-        return self.astype(object)
-
     def _convert_tolerance(self, tolerance, target):
         tolerance = np.asarray(to_timedelta(tolerance).to_numpy())
 
@@ -612,7 +589,8 @@ def intersection(self, other, sort=False):
             result = Index.intersection(self, other, sort=sort)
             if isinstance(result, type(self)):
                 if result.freq is None:
-                    result.freq = to_offset(result.inferred_freq)
+                    # TODO: find a less code-smelly way to set this
+                    result._data._freq = to_offset(result.inferred_freq)
             return result
 
         elif (
@@ -626,7 +604,9 @@ def intersection(self, other, sort=False):
 
             # Invalidate the freq of `result`, which may not be correct at
             # this point, depending on the values.
-            result.freq = None
+
+            # TODO: find a less code-smelly way to set this
+            result._data._freq = None
             if hasattr(self, "tz"):
                 result = self._shallow_copy(
                     result._values, name=result.name, tz=result.tz, freq=None
@@ -634,7 +614,8 @@ def intersection(self, other, sort=False):
             else:
                 result = self._shallow_copy(result._values, name=result.name, freq=None)
             if result.freq is None:
-                result.freq = to_offset(result.inferred_freq)
+                # TODO: find a less code-smelly way to set this
+                result._data._freq = to_offset(result.inferred_freq)
             return result
 
         # to make our life easier, "sort" the two ranges
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index b6891bc7e2b59..ab9f57ff9ac69 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -467,7 +467,7 @@ def _convert_for_op(self, value):
     @Appender(Index.difference.__doc__)
     def difference(self, other, sort=None):
         new_idx = super().difference(other, sort=sort)
-        new_idx.freq = None
+        new_idx._data._freq = None
         return new_idx
 
     # --------------------------------------------------------------------
@@ -522,7 +522,7 @@ def _union(self, other, sort):
                 if result.freq is None and (
                     this.freq is not None or other.freq is not None
                 ):
-                    result.freq = to_offset(result.inferred_freq)
+                    result._data._freq = to_offset(result.inferred_freq)
             return result
 
     def union_many(self, others):
@@ -1208,7 +1208,7 @@ def offset(self, value):
             )
         )
         warnings.warn(msg, FutureWarning, stacklevel=2)
-        self.freq = value
+        self._data.freq = value
 
     def __getitem__(self, key):
         result = self._data.__getitem__(key)
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index cae1380e930f1..cdd0e600c888d 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -313,21 +313,6 @@ def values(self):
     def freq(self) -> DateOffset:
         return self._data.freq
 
-    @freq.setter
-    def freq(self, value):
-        value = Period._maybe_convert_freq(value)
-        # TODO: When this deprecation is enforced, PeriodIndex.freq can
-        # be removed entirely, and we'll just inherit.
-        msg = (
-            "Setting {cls}.freq has been deprecated and will be "
-            "removed in a future version; use {cls}.asfreq instead. "
-            "The {cls}.freq setter is not guaranteed to work."
-        )
-        warnings.warn(msg.format(cls=type(self).__name__), FutureWarning, stacklevel=2)
-        # PeriodArray._freq isn't actually mutable. We set the private _freq
-        # here, but people shouldn't be doing this anyway.
-        self._data._freq = value
-
     def _shallow_copy(self, values=None, **kwargs):
         # TODO: simplify, figure out type of values
         if values is None:
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index 1fd824235c2be..7a7720f730312 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -356,7 +356,8 @@ def _union(self, other, sort):
             result = Index._union(this, other, sort=sort)
             if isinstance(result, TimedeltaIndex):
                 if result.freq is None:
-                    result.freq = to_offset(result.inferred_freq)
+                    # TODO: find a less code-smelly way to set this
+                    result._data._freq = to_offset(result.inferred_freq)
             return result
 
     def join(self, other, how="left", level=None, return_indexers=False, sort=False):
@@ -409,7 +410,8 @@ def intersection(self, other, sort=False):
     @Appender(Index.difference.__doc__)
     def difference(self, other, sort=None):
         new_idx = super().difference(other, sort=sort)
-        new_idx.freq = None
+        # TODO: find a less code-smelly way to set this
+        new_idx._data._freq = None
         return new_idx
 
     def _wrap_joined_index(self, joined, other):
diff --git a/pandas/core/resample.py b/pandas/core/resample.py
index 25731c4e1c54c..2433e3f52b4a9 100644
--- a/pandas/core/resample.py
+++ b/pandas/core/resample.py
@@ -1080,7 +1080,8 @@ def _downsample(self, how, **kwargs):
         if not len(ax):
             # reset to the new freq
             obj = obj.copy()
-            obj.index.freq = self.freq
+            # TODO: find a less code-smelly way to set this
+            obj.index._data._freq = self.freq
             return obj
 
         # do we have a regular frequency
diff --git a/pandas/tests/arrays/categorical/test_constructors.py b/pandas/tests/arrays/categorical/test_constructors.py
index 6eb26d26e14bd..59017a1442cb4 100644
--- a/pandas/tests/arrays/categorical/test_constructors.py
+++ b/pandas/tests/arrays/categorical/test_constructors.py
@@ -311,7 +311,7 @@ def test_constructor_with_datetimelike(self, dtl):
         c = Categorical(s)
 
         expected = type(dtl)(s)
-        expected.freq = None
+        expected._data.freq = None
 
         tm.assert_index_equal(c.categories, expected)
         tm.assert_numpy_array_equal(c.codes, np.arange(5, dtype="int8"))
@@ -322,7 +322,7 @@ def test_constructor_with_datetimelike(self, dtl):
         c = Categorical(s2)
 
         expected = type(dtl)(s2.dropna())
-        expected.freq = None
+        expected._data.freq = None
 
         tm.assert_index_equal(c.categories, expected)
 
diff --git a/pandas/tests/indexes/datetimelike.py b/pandas/tests/indexes/datetimelike.py
index f7cded9f44918..e6e38ce9921f5 100644
--- a/pandas/tests/indexes/datetimelike.py
+++ b/pandas/tests/indexes/datetimelike.py
@@ -81,7 +81,7 @@ def test_map_dictlike(self, mapper):
 
         # don't compare the freqs
         if isinstance(expected, pd.DatetimeIndex):
-            expected.freq = None
+            expected._data.freq = None
 
         result = index.map(mapper(expected, index))
         tm.assert_index_equal(result, expected)
@@ -95,10 +95,3 @@ def test_map_dictlike(self, mapper):
         expected = pd.Index([np.nan] * len(index))
         result = index.map(mapper([], []))
         tm.assert_index_equal(result, expected)
-
-    def test_asobject_deprecated(self):
-        # GH18572
-        d = self.create_index()
-        with tm.assert_produces_warning(FutureWarning):
-            i = d.asobject
-        assert isinstance(i, pd.Index)
diff --git a/pandas/tests/indexes/datetimes/test_date_range.py b/pandas/tests/indexes/datetimes/test_date_range.py
index ba7e3c9d38861..f95137cd1bf88 100644
--- a/pandas/tests/indexes/datetimes/test_date_range.py
+++ b/pandas/tests/indexes/datetimes/test_date_range.py
@@ -798,7 +798,7 @@ def test_daterange_bug_456(self):
         # GH #456
         rng1 = bdate_range("12/5/2011", "12/5/2011")
         rng2 = bdate_range("12/2/2011", "12/5/2011")
-        rng2.freq = BDay()
+        rng2._data.freq = BDay()  # TODO: shouldnt this already be set?
 
         result = rng1.union(rng2)
         assert isinstance(result, DatetimeIndex)
@@ -855,7 +855,7 @@ def test_daterange_bug_456(self):
         # GH #456
         rng1 = bdate_range("12/5/2011", "12/5/2011", freq="C")
         rng2 = bdate_range("12/2/2011", "12/5/2011", freq="C")
-        rng2.freq = CDay()
+        rng2._data.freq = CDay()  # TODO: shouldnt this already be set?
 
         result = rng1.union(rng2)
         assert isinstance(result, DatetimeIndex)
diff --git a/pandas/tests/indexes/datetimes/test_ops.py b/pandas/tests/indexes/datetimes/test_ops.py
index 2944767ba4c02..c9c5963e5590c 100644
--- a/pandas/tests/indexes/datetimes/test_ops.py
+++ b/pandas/tests/indexes/datetimes/test_ops.py
@@ -413,12 +413,12 @@ def test_freq_setter(self, values, freq, tz):
         idx = DatetimeIndex(values, tz=tz)
 
         # can set to an offset, converting from string if necessary
-        idx.freq = freq
+        idx._data.freq = freq
         assert idx.freq == freq
         assert isinstance(idx.freq, ABCDateOffset)
 
         # can reset to None
-        idx.freq = None
+        idx._data.freq = None
         assert idx.freq is None
 
     def test_freq_setter_errors(self):
@@ -431,11 +431,11 @@ def test_freq_setter_errors(self):
             "passed frequency 5D"
         )
         with pytest.raises(ValueError, match=msg):
-            idx.freq = "5D"
+            idx._data.freq = "5D"
 
         # setting with non-freq string
         with pytest.raises(ValueError, match="Invalid frequency"):
-            idx.freq = "foo"
+            idx._data.freq = "foo"
 
     def test_offset_deprecated(self):
         # GH 20716
diff --git a/pandas/tests/indexes/datetimes/test_setops.py b/pandas/tests/indexes/datetimes/test_setops.py
index 67fc70c17d7bc..3fb39b2081d83 100644
--- a/pandas/tests/indexes/datetimes/test_setops.py
+++ b/pandas/tests/indexes/datetimes/test_setops.py
@@ -157,7 +157,7 @@ def test_union_bug_4564(self, sort):
     def test_union_freq_both_none(self, sort):
         # GH11086
         expected = bdate_range("20150101", periods=10)
-        expected.freq = None
+        expected._data.freq = None
 
         result = expected.union(expected, sort=sort)
         tm.assert_index_equal(result, expected)
diff --git a/pandas/tests/indexes/period/test_ops.py b/pandas/tests/indexes/period/test_ops.py
index 96042f4dbaba2..6690a8207eb58 100644
--- a/pandas/tests/indexes/period/test_ops.py
+++ b/pandas/tests/indexes/period/test_ops.py
@@ -343,5 +343,5 @@ def test_freq_setter_deprecated(self):
             idx.freq
 
         # warning for setter
-        with tm.assert_produces_warning(FutureWarning):
+        with pytest.raises(AttributeError, match="can't set attribute"):
             idx.freq = pd.offsets.Day()
diff --git a/pandas/tests/indexes/timedeltas/test_ops.py b/pandas/tests/indexes/timedeltas/test_ops.py
index 54ed5058b5253..df448f4332d38 100644
--- a/pandas/tests/indexes/timedeltas/test_ops.py
+++ b/pandas/tests/indexes/timedeltas/test_ops.py
@@ -286,12 +286,12 @@ def test_freq_setter(self, values, freq):
         idx = TimedeltaIndex(values)
 
         # can set to an offset, converting from string if necessary
-        idx.freq = freq
+        idx._data.freq = freq
         assert idx.freq == freq
         assert isinstance(idx.freq, ABCDateOffset)
 
         # can reset to None
-        idx.freq = None
+        idx._data.freq = None
         assert idx.freq is None
 
     def test_freq_setter_errors(self):
@@ -304,13 +304,13 @@ def test_freq_setter_errors(self):
             "passed frequency 5D"
         )
         with pytest.raises(ValueError, match=msg):
-            idx.freq = "5D"
+            idx._data.freq = "5D"
 
         # setting with a non-fixed frequency
         msg = r"<2 \* BusinessDays> is a non-fixed frequency"
         with pytest.raises(ValueError, match=msg):
-            idx.freq = "2B"
+            idx._data.freq = "2B"
 
         # setting with non-freq string
         with pytest.raises(ValueError, match="Invalid frequency"):
-            idx.freq = "foo"
+            idx._data.freq = "foo"
diff --git a/pandas/tests/reshape/test_concat.py b/pandas/tests/reshape/test_concat.py
index 323b3126c2461..795bbabdfad50 100644
--- a/pandas/tests/reshape/test_concat.py
+++ b/pandas/tests/reshape/test_concat.py
@@ -2774,5 +2774,5 @@ def test_concat_datetimeindex_freq():
     # Non-monotonic index result
     result = pd.concat([expected[50:], expected[:50]])
     expected = pd.DataFrame(data[50:] + data[:50], index=dr[50:].append(dr[:50]))
-    expected.index.freq = None
+    expected.index._data.freq = None
     tm.assert_frame_equal(result, expected)