diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index e577a8f26bd12..eb43ccd3429aa 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -104,7 +104,7 @@ Other enhancements
 - :meth:`DataFrame.applymap` now supports ``na_action`` (:issue:`23803`)
 - :class:`Index` with object dtype supports division and multiplication (:issue:`34160`)
 - :meth:`DataFrame.explode` and :meth:`Series.explode` now support exploding of sets (:issue:`35614`)
--
+- `Styler` now allows direct CSS class name addition to individual data cells (:issue:`36159`)
 
 .. _whatsnew_120.api_breaking.python:
 
diff --git a/pandas/io/formats/style.py b/pandas/io/formats/style.py
index b27a4e036e137..5c3a309b0e310 100644
--- a/pandas/io/formats/style.py
+++ b/pandas/io/formats/style.py
@@ -171,6 +171,8 @@ def __init__(
         self.cell_ids = cell_ids
         self.na_rep = na_rep
 
+        self.cell_context: Dict[str, Any] = {}
+
         # display_funcs maps (row, col) -> formatting function
 
         def default_display_func(x):
@@ -262,7 +264,7 @@ def format_attr(pair):
         idx_lengths = _get_level_lengths(self.index)
         col_lengths = _get_level_lengths(self.columns, hidden_columns)
 
-        cell_context = dict()
+        cell_context = self.cell_context
 
         n_rlvls = self.data.index.nlevels
         n_clvls = self.data.columns.nlevels
@@ -499,6 +501,70 @@ def format(self, formatter, subset=None, na_rep: Optional[str] = None) -> "Style
                 self._display_funcs[(i, j)] = formatter
         return self
 
+    def set_td_classes(self, classes: DataFrame) -> "Styler":
+        """
+        Add string based CSS class names to data cells that will appear within the
+        `Styler` HTML result. These classes are added within specified `<td>` elements.
+
+        Parameters
+        ----------
+        classes : DataFrame
+            DataFrame containing strings that will be translated to CSS classes,
+            mapped by identical column and index values that must exist on the
+            underlying `Styler` data. None, NaN values, and empty strings will
+            be ignored and not affect the rendered HTML.
+
+        Returns
+        -------
+        self : Styler
+
+        Examples
+        --------
+        >>> df = pd.DataFrame(data=[[1, 2, 3], [4, 5, 6]], columns=["A", "B", "C"])
+        >>> classes = pd.DataFrame([
+        ...     ["min-val red", "", "blue"],
+        ...     ["red", None, "blue max-val"]
+        ... ], index=df.index, columns=df.columns)
+        >>> df.style.set_td_classes(classes)
+
+        Using `MultiIndex` columns and a `classes` `DataFrame` as a subset of the
+        underlying,
+
+        >>> df = pd.DataFrame([[1,2],[3,4]], index=["a", "b"],
+        ...     columns=[["level0", "level0"], ["level1a", "level1b"]])
+        >>> classes = pd.DataFrame(["min-val"], index=["a"],
+        ...     columns=[["level0"],["level1a"]])
+        >>> df.style.set_td_classes(classes)
+
+        Form of the output with new additional css classes,
+
+        >>> df = pd.DataFrame([[1]])
+        >>> css = pd.DataFrame(["other-class"])
+        >>> s = Styler(df, uuid="_", cell_ids=False).set_td_classes(css)
+        >>> s.hide_index().render()
+        '<style  type="text/css" ></style>'
+        '<table id="T__" >'
+        '  <thead>'
+        '    <tr><th class="col_heading level0 col0" >0</th></tr>'
+        '  </thead>'
+        '  <tbody>'
+        '    <tr><td  class="data row0 col0 other-class" >1</td></tr>'
+        '  </tbody>'
+        '</table>'
+
+        """
+        classes = classes.reindex_like(self.data)
+
+        mask = (classes.isna()) | (classes.eq(""))
+        self.cell_context["data"] = {
+            r: {c: [str(classes.iloc[r, c])]}
+            for r, rn in enumerate(classes.index)
+            for c, cn in enumerate(classes.columns)
+            if not mask.iloc[r, c]
+        }
+
+        return self
+
     def render(self, **kwargs) -> str:
         """
         Render the built up styles to HTML.
@@ -609,6 +675,7 @@ def clear(self) -> None:
         Returns None.
         """
         self.ctx.clear()
+        self.cell_context = {}
         self._todo = []
 
     def _compute(self):
diff --git a/pandas/tests/io/formats/test_style.py b/pandas/tests/io/formats/test_style.py
index de549ec3eb75e..e7583e1ce2ce2 100644
--- a/pandas/tests/io/formats/test_style.py
+++ b/pandas/tests/io/formats/test_style.py
@@ -1691,6 +1691,27 @@ def test_no_cell_ids(self):
         s = styler.render()  # render twice to ensure ctx is not updated
         assert s.find('<td  class="data row0 col0" >') != -1
 
+    @pytest.mark.parametrize(
+        "classes",
+        [
+            DataFrame(
+                data=[["", "test-class"], [np.nan, None]],
+                columns=["A", "B"],
+                index=["a", "b"],
+            ),
+            DataFrame(data=[["test-class"]], columns=["B"], index=["a"]),
+            DataFrame(data=[["test-class", "unused"]], columns=["B", "C"], index=["a"]),
+        ],
+    )
+    def test_set_data_classes(self, classes):
+        # GH 36159
+        df = DataFrame(data=[[0, 1], [2, 3]], columns=["A", "B"], index=["a", "b"])
+        s = Styler(df, uuid="_", cell_ids=False).set_td_classes(classes).render()
+        assert '<td  class="data row0 col0" >0</td>' in s
+        assert '<td  class="data row0 col1 test-class" >1</td>' in s
+        assert '<td  class="data row1 col0" >2</td>' in s
+        assert '<td  class="data row1 col1" >3</td>' in s
+
     def test_colspan_w3(self):
         # GH 36223
         df = pd.DataFrame(data=[[1, 2]], columns=[["l0", "l0"], ["l1a", "l1b"]])