diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 7ce60dc6e81..dbd3ebbfe7e 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -24,10 +24,13 @@ This release increases the minimum required Python version from 3.5.0 to 3.5.3
 Breaking changes
 ~~~~~~~~~~~~~~~~
 
-  The ``isel_points`` and ``sel_points`` methods are removed, having been deprecated
+- The ``isel_points`` and ``sel_points`` methods are removed, having been deprecated
   since v0.10.0. These are redundant with the ``isel`` / ``sel`` methods.
   See :ref:`vectorized_indexing` for the details 
   By `Maximilian Roos <https://github.com/max-sixty>`_ 
+- The ``inplace`` kwarg for public methods now raises an error, having been deprecated
+  since v0.11.0.
+  By `Maximilian Roos <https://github.com/max-sixty>`_ 
 
 New functions/methods
 ~~~~~~~~~~~~~~~~~~~~~
diff --git a/xarray/core/dataarray.py b/xarray/core/dataarray.py
index 4bd80553588..e3e543b6621 100644
--- a/xarray/core/dataarray.py
+++ b/xarray/core/dataarray.py
@@ -700,30 +700,17 @@ def reset_coords(
         drop : bool, optional
             If True, remove coordinates instead of converting them into
             variables.
-        inplace : bool, optional
-            If True, modify this object in place. Otherwise, create a new
-            object.
 
         Returns
         -------
-        Dataset, or DataArray if ``drop == True``, or None if
-        ``inplace == True``
+        Dataset, or DataArray if ``drop == True``
         """
-        inplace = _check_inplace(inplace)
-        if inplace and not drop:
-            raise ValueError(
-                "cannot reset coordinates in-place on a "
-                "DataArray without ``drop == True``"
-            )
+        _check_inplace(inplace)
         if names is None:
             names = set(self.coords) - set(self.dims)
         dataset = self.coords.to_dataset().reset_coords(names, drop)
         if drop:
-            if inplace:
-                self._coords = dataset._variables
-                return None
-            else:
-                return self._replace(coords=dataset._variables)
+            return self._replace(coords=dataset._variables)
         else:
             if self.name is None:
                 raise ValueError(
@@ -1485,9 +1472,6 @@ def set_index(
         append : bool, optional
             If True, append the supplied index(es) to the existing index(es).
             Otherwise replace the existing index(es) (default).
-        inplace : bool, optional
-            If True, set new index(es) in-place. Otherwise, return a new
-            DataArray object.
         **indexes_kwargs: optional
             The keyword arguments form of ``indexes``.
             One of indexes or indexes_kwargs must be provided.
@@ -1496,7 +1480,6 @@ def set_index(
         -------
         obj : DataArray
             Another DataArray, with this data but replaced coordinates.
-            Return None if inplace=True.
 
         Example
         -------
@@ -1526,14 +1509,10 @@ def set_index(
         --------
         DataArray.reset_index
         """
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         indexes = either_dict_or_kwargs(indexes, indexes_kwargs, "set_index")
         coords, _ = merge_indexes(indexes, self._coords, set(), append=append)
-        if inplace:
-            self._coords = coords
-            return None
-        else:
-            return self._replace(coords=coords)
+        return self._replace(coords=coords)
 
     def reset_index(
         self,
@@ -1551,36 +1530,29 @@ def reset_index(
         drop : bool, optional
             If True, remove the specified indexes and/or multi-index levels
             instead of extracting them as new coordinates (default: False).
-        inplace : bool, optional
-            If True, modify the dataarray in-place. Otherwise, return a new
-            DataArray object.
 
         Returns
         -------
         obj : DataArray
             Another dataarray, with this dataarray's data but replaced
-            coordinates. If ``inplace == True``, return None.
+            coordinates.
 
         See Also
         --------
         DataArray.set_index
         """
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         coords, _ = split_indexes(
             dims_or_levels, self._coords, set(), self._level_coords, drop=drop
         )
-        if inplace:
-            self._coords = coords
-            return None
-        else:
-            return self._replace(coords=coords)
+        return self._replace(coords=coords)
 
     def reorder_levels(
         self,
         dim_order: Mapping[Hashable, Sequence[int]] = None,
         inplace: bool = None,
         **dim_order_kwargs: Sequence[int]
-    ) -> Optional["DataArray"]:
+    ) -> "DataArray":
         """Rearrange index levels using input order.
 
         Parameters
@@ -1589,9 +1561,6 @@ def reorder_levels(
             Mapping from names matching dimensions and values given
             by lists representing new level orders. Every given dimension
             must have a multi-index.
-        inplace : bool, optional
-            If True, modify the dataarray in-place. Otherwise, return a new
-            DataArray object.
         **dim_order_kwargs: optional
             The keyword arguments form of ``dim_order``.
             One of dim_order or dim_order_kwargs must be provided.
@@ -1600,9 +1569,9 @@ def reorder_levels(
         -------
         obj : DataArray
             Another dataarray, with this dataarray's data but replaced
-            coordinates. If ``inplace == True``, return None.
+            coordinates.
         """
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         dim_order = either_dict_or_kwargs(dim_order, dim_order_kwargs, "reorder_levels")
         replace_coords = {}
         for dim, order in dim_order.items():
@@ -1613,11 +1582,7 @@ def reorder_levels(
             replace_coords[dim] = IndexVariable(coord.dims, index.reorder_levels(order))
         coords = self._coords.copy()
         coords.update(replace_coords)
-        if inplace:
-            self._coords = coords
-            return None
-        else:
-            return self._replace(coords=coords)
+        return self._replace(coords=coords)
 
     def stack(
         self,
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 4cb5d1454ce..e62b6612ae6 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -1354,9 +1354,6 @@ def set_coords(
         ----------
         names : hashable or iterable of hashables
             Name(s) of variables in this dataset to convert into coordinates.
-        inplace : bool, optional
-            If True, modify this dataset inplace. Otherwise, create a new
-            object.
 
         Returns
         -------
@@ -1370,13 +1367,13 @@ def set_coords(
         # DataFrame.set_index?
         # nb. check in self._variables, not self.data_vars to insure that the
         # operation is idempotent
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         if isinstance(names, str) or not isinstance(names, Iterable):
             names = [names]
         else:
             names = list(names)
         self._assert_all_in_dataset(names)
-        obj = self if inplace else self.copy()
+        obj = self.copy()
         obj._coord_names.update(names)
         return obj
 
@@ -1396,15 +1393,12 @@ def reset_coords(
         drop : bool, optional
             If True, remove coordinates instead of converting them into
             variables.
-        inplace : bool, optional
-            If True, modify this dataset inplace. Otherwise, create a new
-            object.
 
         Returns
         -------
         Dataset
         """
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         if names is None:
             names = self._coord_names - set(self.dims)
         else:
@@ -1418,7 +1412,7 @@ def reset_coords(
                 raise ValueError(
                     "cannot remove index coordinates with reset_coords: %s" % bad_coords
                 )
-        obj = self if inplace else self.copy()
+        obj = self.copy()
         obj._coord_names.difference_update(names)
         if drop:
             for name in names:
@@ -2397,9 +2391,6 @@ def rename(
         name_dict : dict-like, optional
             Dictionary whose keys are current variable or dimension names and
             whose values are the desired names.
-        inplace : bool, optional
-            If True, rename variables and dimensions in-place. Otherwise,
-            return a new dataset object.
         **names, optional
             Keyword form of ``name_dict``.
             One of name_dict or names must be provided.
@@ -2416,7 +2407,7 @@ def rename(
         Dataset.rename_dims
         DataArray.rename
         """
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         name_dict = either_dict_or_kwargs(name_dict, names, "rename")
         for k in name_dict.keys():
             if k not in self and k not in self.dims:
@@ -2428,9 +2419,7 @@ def rename(
         variables, coord_names, dims, indexes = self._rename_all(
             name_dict=name_dict, dims_dict=name_dict
         )
-        return self._replace(
-            variables, coord_names, dims=dims, indexes=indexes, inplace=inplace
-        )
+        return self._replace(variables, coord_names, dims=dims, indexes=indexes)
 
     def rename_dims(
         self, dims_dict: Mapping[Hashable, Hashable] = None, **dims: Hashable
@@ -2520,9 +2509,6 @@ def swap_dims(
             Dictionary whose keys are current dimension names and whose values
             are new names. Each value must already be a variable in the
             dataset.
-        inplace : bool, optional
-            If True, swap dimensions in-place. Otherwise, return a new dataset
-            object.
 
         Returns
         -------
@@ -2537,7 +2523,7 @@ def swap_dims(
         """
         # TODO: deprecate this method in favor of a (less confusing)
         # rename_dims() method that only renames dimensions.
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         for k, v in dims_dict.items():
             if k not in self.dims:
                 raise ValueError(
@@ -2570,9 +2556,7 @@ def swap_dims(
             var.dims = dims
             variables[k] = var
 
-        return self._replace_with_new_dims(
-            variables, coord_names, indexes=indexes, inplace=inplace
-        )
+        return self._replace_with_new_dims(variables, coord_names, indexes=indexes)
 
     def expand_dims(
         self,
@@ -2746,9 +2730,6 @@ def set_index(
         append : bool, optional
             If True, append the supplied index(es) to the existing index(es).
             Otherwise replace the existing index(es) (default).
-        inplace : bool, optional
-            If True, set new index(es) in-place. Otherwise, return a new
-            Dataset object.
         **indexes_kwargs: optional
             The keyword arguments form of ``indexes``.
             One of indexes or indexes_kwargs must be provided.
@@ -2790,14 +2771,12 @@ def set_index(
         Dataset.reset_index
         Dataset.swap_dims
         """
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         indexes = either_dict_or_kwargs(indexes, indexes_kwargs, "set_index")
         variables, coord_names = merge_indexes(
             indexes, self._variables, self._coord_names, append=append
         )
-        return self._replace_vars_and_dims(
-            variables, coord_names=coord_names, inplace=inplace
-        )
+        return self._replace_vars_and_dims(variables, coord_names=coord_names)
 
     def reset_index(
         self,
@@ -2815,9 +2794,6 @@ def reset_index(
         drop : bool, optional
             If True, remove the specified indexes and/or multi-index levels
             instead of extracting them as new coordinates (default: False).
-        inplace : bool, optional
-            If True, modify the dataset in-place. Otherwise, return a new
-            Dataset object.
 
         Returns
         -------
@@ -2828,7 +2804,7 @@ def reset_index(
         --------
         Dataset.set_index
         """
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         variables, coord_names = split_indexes(
             dims_or_levels,
             self._variables,
@@ -2836,9 +2812,7 @@ def reset_index(
             cast(Mapping[Hashable, Hashable], self._level_coords),
             drop=drop,
         )
-        return self._replace_vars_and_dims(
-            variables, coord_names=coord_names, inplace=inplace
-        )
+        return self._replace_vars_and_dims(variables, coord_names=coord_names)
 
     def reorder_levels(
         self,
@@ -2854,9 +2828,6 @@ def reorder_levels(
             Mapping from names matching dimensions and values given
             by lists representing new level orders. Every given dimension
             must have a multi-index.
-        inplace : bool, optional
-            If True, modify the dataset in-place. Otherwise, return a new
-            DataArray object.
         **dim_order_kwargs: optional
             The keyword arguments form of ``dim_order``.
             One of dim_order or dim_order_kwargs must be provided.
@@ -2867,7 +2838,7 @@ def reorder_levels(
             Another dataset, with this dataset's data but replaced
             coordinates.
         """
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         dim_order = either_dict_or_kwargs(dim_order, dim_order_kwargs, "reorder_levels")
         variables = self._variables.copy()
         indexes = OrderedDict(self.indexes)
@@ -2880,7 +2851,7 @@ def reorder_levels(
             variables[dim] = IndexVariable(coord.dims, new_index)
             indexes[dim] = new_index
 
-        return self._replace(variables, indexes=indexes, inplace=inplace)
+        return self._replace(variables, indexes=indexes)
 
     def _stack_once(self, dims, new_dim):
         variables = OrderedDict()
@@ -3176,9 +3147,6 @@ def update(self, other: "DatasetLike", inplace: bool = None) -> "Dataset":
             - mapping {var name: (dimension name, array-like)}
             - mapping {var name: (tuple of dimension names, array-like)}
 
-        inplace : bool, optional
-            If True, merge the other dataset into this dataset in-place.
-            Otherwise, return a new dataset object.
 
         Returns
         -------
@@ -3191,12 +3159,10 @@ def update(self, other: "DatasetLike", inplace: bool = None) -> "Dataset":
             If any dimensions would have inconsistent sizes in the updated
             dataset.
         """
-        inplace = _check_inplace(inplace, default=True)
+        _check_inplace(inplace)
         variables, coord_names, dims = dataset_update_method(self, other)
 
-        return self._replace_vars_and_dims(
-            variables, coord_names, dims, inplace=inplace
-        )
+        return self._replace_vars_and_dims(variables, coord_names, dims, inplace=True)
 
     def merge(
         self,
@@ -3218,9 +3184,6 @@ def merge(
         ----------
         other : Dataset or castable to Dataset
             Dataset or variables to merge with this dataset.
-        inplace : bool, optional
-            If True, merge the other dataset into this dataset in-place.
-            Otherwise, return a new dataset object.
         overwrite_vars : Hashable or iterable of Hashable, optional
             If provided, update variables of these name(s) without checking for
             conflicts in this dataset.
@@ -3257,7 +3220,7 @@ def merge(
         MergeError
             If any variables conflict (see ``compat``).
         """
-        inplace = _check_inplace(inplace)
+        _check_inplace(inplace)
         variables, coord_names, dims = dataset_merge_method(
             self,
             other,
@@ -3267,9 +3230,7 @@ def merge(
             fill_value=fill_value,
         )
 
-        return self._replace_vars_and_dims(
-            variables, coord_names, dims, inplace=inplace
-        )
+        return self._replace_vars_and_dims(variables, coord_names, dims)
 
     def _assert_all_in_dataset(
         self, names: Iterable[Hashable], virtual_okay: bool = False
diff --git a/xarray/core/utils.py b/xarray/core/utils.py
index bf8c9a264e3..a8bb5532f1f 100644
--- a/xarray/core/utils.py
+++ b/xarray/core/utils.py
@@ -36,19 +36,13 @@
 T = TypeVar("T")
 
 
-def _check_inplace(inplace: Optional[bool], default: bool = False) -> bool:
-    if inplace is None:
-        inplace = default
-    else:
-        warnings.warn(
-            "The inplace argument has been deprecated and will be "
-            "removed in a future version of xarray.",
-            FutureWarning,
-            stacklevel=3,
+def _check_inplace(inplace: Optional[bool]) -> None:
+    if inplace is not None:
+        raise TypeError(
+            "The `inplace` argument has been removed from xarray. "
+            "You can achieve an identical effect with python's standard assignment."
         )
 
-    return inplace
-
 
 def alias_message(old_name: str, new_name: str) -> str:
     return "%s has been deprecated. Use %s instead." % (old_name, new_name)
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 6a68fb73837..798ef66c82e 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -1291,9 +1291,8 @@ def test_reset_coords(self):
         )
         assert_identical(actual, expected)
 
-        with pytest.warns(FutureWarning, match="The inplace argument"):
-            with raises_regex(ValueError, "cannot reset coord"):
-                data = data.reset_coords(inplace=True)
+        with pytest.raises(TypeError):
+            data = data.reset_coords(inplace=True)
         with raises_regex(ValueError, "cannot be found"):
             data.reset_coords("foo", drop=True)
         with raises_regex(ValueError, "cannot be found"):
@@ -1702,10 +1701,9 @@ def test_reorder_levels(self):
         obj = self.mda.reorder_levels(x=["level_2", "level_1"])
         assert_identical(obj, expected)
 
-        with pytest.warns(FutureWarning, match="The inplace argument"):
+        with pytest.raises(TypeError):
             array = self.mda.copy()
             array.reorder_levels(x=["level_2", "level_1"], inplace=True)
-            assert_identical(array, expected)
 
         array = DataArray([1, 2], dims="x")
         with pytest.raises(KeyError):
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 82ae65d955f..a5d9a65d020 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -2325,18 +2325,11 @@ def test_rename_same_name(self):
         renamed = data.rename(newnames)
         assert_identical(renamed, data)
 
-    @pytest.mark.filterwarnings("ignore:The inplace argument")
     def test_rename_inplace(self):
         times = pd.date_range("2000-01-01", periods=3)
         data = Dataset({"z": ("x", [2, 3, 4]), "t": ("t", times)})
-        copied = data.copy()
-        renamed = data.rename({"x": "y"})
-        data.rename({"x": "y"}, inplace=True)
-        assert_identical(data, renamed)
-        assert not data.equals(copied)
-        assert data.dims == {"y": 3, "t": 3}
-        # check virtual variables
-        assert_array_equal(data["t.dayofyear"], [1, 2, 3])
+        with pytest.raises(TypeError):
+            data.rename({"x": "y"}, inplace=True)
 
     def test_rename_dims(self):
         original = Dataset({"x": ("x", [0, 1, 2]), "y": ("x", [10, 11, 12]), "z": 42})
@@ -2599,7 +2592,7 @@ def test_set_index(self):
         obj = ds.set_index(x=mindex.names)
         assert_identical(obj, expected)
 
-        with pytest.warns(FutureWarning, match="The inplace argument"):
+        with pytest.raises(TypeError):
             ds.set_index(x=mindex.names, inplace=True)
             assert_identical(ds, expected)
 
@@ -2624,9 +2617,8 @@ def test_reset_index(self):
         obj = ds.reset_index("x")
         assert_identical(obj, expected)
 
-        with pytest.warns(FutureWarning, match="The inplace argument"):
+        with pytest.raises(TypeError):
             ds.reset_index("x", inplace=True)
-            assert_identical(ds, expected)
 
     def test_reorder_levels(self):
         ds = create_test_multiindex()
@@ -2637,9 +2629,8 @@ def test_reorder_levels(self):
         reindexed = ds.reorder_levels(x=["level_2", "level_1"])
         assert_identical(reindexed, expected)
 
-        with pytest.warns(FutureWarning, match="The inplace argument"):
+        with pytest.raises(TypeError):
             ds.reorder_levels(x=["level_2", "level_1"], inplace=True)
-            assert_identical(ds, expected)
 
         ds = Dataset({}, coords={"x": [1, 2]})
         with raises_regex(ValueError, "has no MultiIndex"):
@@ -2779,11 +2770,8 @@ def test_update(self):
         assert actual_result is actual
         assert_identical(expected, actual)
 
-        with pytest.warns(FutureWarning, match="The inplace argument"):
+        with pytest.raises(TypeError):
             actual = data.update(data, inplace=False)
-            expected = data
-            assert actual is not expected
-            assert_identical(expected, actual)
 
         other = Dataset(attrs={"new": "attr"})
         actual = data.copy()