diff --git a/src/akimbo/apply_tree.py b/src/akimbo/apply_tree.py
index 9aed44d..a6531a7 100644
--- a/src/akimbo/apply_tree.py
+++ b/src/akimbo/apply_tree.py
@@ -8,11 +8,22 @@
 import pyarrow as pa
 
 
+def match_any(*layout, **_):
+    return True
+
+
 def leaf(*layout, **_):
     """True for the lowest elements of any akwward layout tree"""
     return layout[0].is_leaf
 
 
+def numeric(*layout, **_):
+    return layout[0].is_leaf and layout[0].parameters.get("__array__", None) not in {
+        "string",
+        "char",
+    }
+
+
 def run_with_transform(
     arr: ak.Array,
     op,
@@ -24,6 +35,8 @@ def run_with_transform(
     **kw,
 ) -> ak.Array:
     def func(layout, **kwargs):
+        from akimbo.utils import match_string
+
         if not isinstance(layout, tuple):
             layout = (layout,)
         if all(match(lay, **(match_kwargs or {})) for lay in layout):
@@ -34,11 +47,23 @@ def func(layout, **kwargs):
             elif inmode == "numpy":
                 # works on numpy/cupy contents
                 out = op(*(lay.data for lay in layout), **kw, **(match_kwargs or {}))
-            else:
+            elif inmode == "ak":
                 out = op(*layout, **kw, **(match_kwargs or {}))
-            return outtype(out) if callable(outtype) else out
+            else:
+                out = op(
+                    *(ak.Array(lay) for lay in layout), **kw, **(match_kwargs or {})
+                )
+            if callable(outtype):
+                return outtype(out)
+            elif isinstance(out, ak.Array):
+                return out.layout
+            else:
+                return out
+        if match_string(*layout):
+            # non-string op may fail to descend into string
+            return layout[0]
 
-    return ak.transform(func, arr, *others)
+    return ak.transform(func, arr, *others, allow_records=True)
 
 
 def dec(
diff --git a/src/akimbo/mixin.py b/src/akimbo/mixin.py
index 82faf73..c123ab6 100644
--- a/src/akimbo/mixin.py
+++ b/src/akimbo/mixin.py
@@ -7,7 +7,8 @@
 import awkward as ak
 import pyarrow.compute as pc
 
-from akimbo.apply_tree import dec
+from akimbo.apply_tree import dec, match_any, numeric, run_with_transform
+from akimbo.utils import to_ak_layout
 
 methods = [
     _ for _ in (dir(ak)) if not _.startswith(("_", "ak_")) and not _[0].isupper()
@@ -179,6 +180,9 @@ def apply(self, fn: Callable, where=None, **kwargs):
 
         The function should take an ak array as input and produce an
         ak array or scalar.
+
+        Unlike ``transform``, the function takes and returns ak.Array instances
+        and acts on a whole schema tree.
         """
         if where:
             bits = tuple(where.split("."))
@@ -190,6 +194,44 @@ def apply(self, fn: Callable, where=None, **kwargs):
             final = fn(self.array)
         return self.to_output(final)
 
+    def transform(
+        self, fn: Callable, *others, where=None, match=match_any, inmode="ak", **kwargs
+    ):
+        """Perform arbitrary function to selected parts of the data tree
+
+        This process walks thought the data's schema tree, and applies the given
+        function only on the matching nodes.
+
+        Parameters
+        ----------
+        fn: the operation you want to perform. Typically unary or binary, and may take
+            extra kwargs
+        others: extra arguments, perhaps other akimbo series
+        where: path in the schema tree to apply this
+        match: when walking the schema, this determines if a node should be processed;
+            it will be a function taking one or more ak.contents classes. ak.apaply_tree
+            contains convenience matchers macth_any, leaf and numeric, and more matchers
+            can be found in the string and datetime modules
+        inmode: data should be passed to the given function as:
+            "arrow" | "numpy" (includes cupy) | "ak" layout | "array" high-level ak.Array
+        kwargs: passed to the operation, except those that are taken by ``run_with_transform``.
+        """
+        if where:
+            bits = tuple(where.split("."))
+            arr = self.array
+            part = arr.__getitem__(bits)
+            # TODO: apply ``where`` to any arrays in others
+            # other = [to_ak_layout(ar) for ar in others]
+            out = run_with_transform(
+                part, fn, match=match, others=others, inmode=inmode, **kwargs
+            )
+            final = ak.with_field(arr, out, where=where)
+        else:
+            final = run_with_transform(
+                self.array, fn, match=match, others=others, inmode=inmode, **kwargs
+            )
+        return self.to_output(final)
+
     def __getitem__(self, item):
         out = self.array.__getitem__(item)
         return self.to_output(out)
@@ -331,12 +373,31 @@ def join(
     def _create_op(cls, op):
         """Make functions to perform all the arithmetic, logical and comparison ops"""
 
-        def run(self, *args, **kwargs):
-            ar2 = (ar.ak.array if hasattr(ar, "ak") else ar for ar in args)
-            ar3 = (ar.array if isinstance(ar, cls) else ar for ar in ar2)
-            return self.to_output(op(self.array, *ar3, **kwargs))
+        def op2(*args, extra=None, **kw):
+            args = list(args) + list(extra or [])
+            return op(*args, **kw)
+
+        def f(self, *args, **kw):
+            # TODO: test here is for literals, but really we want "don't know how to
+            #  array that" condition
+            extra = (_ for _ in args if isinstance(_, (str, int, float)))
+            args = (
+                to_ak_layout(_) for _ in args if not isinstance(_, (str, int, float))
+            )
+            out = self.transform(
+                op2,
+                *args,
+                match=numeric,
+                inmode="numpy",
+                extra=extra,
+                outtype=ak.contents.NumpyArray,
+                **kw,
+            )
+            if isinstance(self._obj, self.dataframe_type):
+                return out.ak.unmerge()
+            return out
 
-        return run
+        return f
 
     def __getattr__(self, item):
         arr = self.array
diff --git a/src/akimbo/strings.py b/src/akimbo/strings.py
index 6e7fcb2..1460154 100644
--- a/src/akimbo/strings.py
+++ b/src/akimbo/strings.py
@@ -8,10 +8,7 @@
 
 from akimbo.apply_tree import dec
 from akimbo.mixin import Accessor
-
-
-def match_string(*layout):
-    return layout[0].is_list and layout[0].parameter("__array__") == "string"
+from akimbo.utils import match_string
 
 
 def _encode(layout):
@@ -53,14 +50,21 @@ def _decode(layout):
 
 # make sensible defaults for strptime
 strptime = functools.wraps(pc.strptime)(
-    lambda *args, format="%FT%T", unit="s", error_is_null=True, **kw:
-        pc.strptime(*args, format=format, unit=unit, error_is_null=error_is_null)
+    lambda *args, format="%FT%T", unit="s", error_is_null=True, **kw: pc.strptime(
+        *args, format=format, unit=unit, error_is_null=error_is_null
+    )
 )
 
 
 class StringAccessor:
     """String operations on nested/var-length data"""
 
+    # TODO: implement dunder add (concat strings) and mul (repeat strings)
+    #  - s.ak.str + "suffix" (and arguments swapped)
+    #  - s.ak.str + s2.ak.str (with matching schemas)
+    #  - s.ak.str * N (and arguments swapped)
+    #  - s.ak.str * s (where each string maps to integers for variable repeats)
+
     def __init__(self, accessor):
         self.accessor = accessor
 
diff --git a/src/akimbo/utils.py b/src/akimbo/utils.py
index cfda842..a5f1b89 100644
--- a/src/akimbo/utils.py
+++ b/src/akimbo/utils.py
@@ -1,3 +1,8 @@
+from __future__ import annotations
+
+import awkward as ak
+
+
 class NoAttributes:
     """Allows importing akimbo.cudf even if cudf isn't installed
 
@@ -20,3 +25,18 @@ def __call__(self, *args, **kwargs):
     __name__ = "DummyAttributesObject"
     __doc__ = None
     __annotations__ = None
+
+
+def to_ak_layout(ar):
+    if hasattr(ar, "ak"):
+        return ar.ak.array
+    elif hasattr(ar, "array"):
+        return ar.array
+    elif isinstance(ar, (ak.Array)):
+        return ar
+    else:
+        return ak.Array(ak.to_layout(ar))
+
+
+def match_string(*layout):
+    return layout[0].is_list and layout[0].parameter("__array__") == "string"
diff --git a/tests/test_pandas.py b/tests/test_pandas.py
index 13ae2b4..2580e59 100644
--- a/tests/test_pandas.py
+++ b/tests/test_pandas.py
@@ -49,6 +49,58 @@ def test_ufunc():
     assert (s.ak + s.ak).tolist() == [[2, 4, 6], [8, 10], [12]]
     assert (s.ak + s).tolist() == [[2, 4, 6], [8, 10], [12]]
 
+    s = pd.DataFrame({"a": s})
+    assert (s.ak + 1).a.tolist() == [[2, 3, 4], [5, 6], [7]]
+
+    assert (s.ak + s.ak).a.tolist() == [[2, 4, 6], [8, 10], [12]]
+    assert (s.ak + s).a.tolist() == [[2, 4, 6], [8, 10], [12]]
+
+
+def test_manual_ufunc():
+    from akimbo.apply_tree import numeric
+
+    df = pd.DataFrame(
+        {"a": [["hey", "hi", "ho"], [None], ["blah"]], "b": [[1, 2, 3], [4, 5], [6]]}
+    )
+    df2 = df.ak.transform(
+        lambda x: x + 1, match=numeric, inmode="numpy", outtype=ak.contents.NumpyArray
+    )
+    expected = [
+        {"a": ["hey", "hi", "ho"], "b": [2, 3, 4]},
+        {"a": [None], "b": [5, 6]},
+        {"a": ["blah"], "b": [7]},
+    ]
+    assert df2.tolist() == expected
+
+
+def test_mixed_ufunc():
+    # ufuncs are numeric only by default, doesn't touch strings
+    df = pd.DataFrame(
+        {"a": [["hey", "hi", "ho"], [None], ["blah"]], "b": [[1, 2, 3], [4, 5], [6]]}
+    )
+    df2 = df.ak + 1
+    expected = [
+        {"a": ["hey", "hi", "ho"], "b": [2, 3, 4]},
+        {"a": [None], "b": [5, 6]},
+        {"a": ["blah"], "b": [7]},
+    ]
+    assert df2.ak.tolist() == expected
+
+    df2 = df.ak * 2
+    expected = [
+        {"a": ["hey", "hi", "ho"], "b": [2, 4, 6]},
+        {"a": [None], "b": [8, 10]},
+        {"a": ["blah"], "b": [12]},
+    ]
+    assert df2.ak.tolist() == expected
+    df2 = 2 * df.ak
+    assert df2.ak.tolist() == expected
+
+    df2 = df.ak == df.ak
+    expected = [[True, True, True], [True, True], [True]]
+    assert df2["b"].tolist() == expected
+    assert df2["a"].tolist() == df["a"].tolist()
+
 
 def test_to_autoarrow():
     a = [[1, 2, 3], [4, 5], [6]]
diff --git a/tests/test_polars.py b/tests/test_polars.py
index 56b5d93..e4180fc 100644
--- a/tests/test_polars.py
+++ b/tests/test_polars.py
@@ -54,3 +54,7 @@ def test_ufunc():
 
     s2 = np.add(s.ak, 1)
     assert s2.to_list() == [[2, 3, 4], [], [5, 6]]
+
+    df = pl.DataFrame({"a": s})
+    df2 = df.ak + 1
+    assert df2["a"].to_list() == [[2, 3, 4], [], [5, 6]]