diff --git a/narwhals/_arrow/dataframe.py b/narwhals/_arrow/dataframe.py
index 94dccd0c5..7526e528a 100644
--- a/narwhals/_arrow/dataframe.py
+++ b/narwhals/_arrow/dataframe.py
@@ -14,6 +14,7 @@
 from narwhals.dependencies import get_pyarrow
 from narwhals.dependencies import get_pyarrow_parquet
 from narwhals.utils import flatten
+from narwhals.utils import generate_unique_token
 
 if TYPE_CHECKING:
     from typing_extensions import Self
@@ -208,7 +209,7 @@ def join(
         self,
         other: Self,
         *,
-        how: Literal["inner"] = "inner",
+        how: Literal["left", "inner", "outer", "cross", "anti", "semi"] = "inner",
         left_on: str | list[str] | None,
         right_on: str | list[str] | None,
     ) -> Self:
@@ -217,24 +218,35 @@ def join(
         if isinstance(right_on, str):
             right_on = [right_on]
 
-        if how == "cross":  # type: ignore[comparison-overlap]
-            raise NotImplementedError
-
-        if how == "anti":  # type: ignore[comparison-overlap]
-            raise NotImplementedError
+        how_to_join_map = {
+            "anti": "left anti",
+            "semi": "left semi",
+            "inner": "inner",
+            "left": "left outer",
+        }
 
-        if how == "semi":  # type: ignore[comparison-overlap]
-            raise NotImplementedError
+        if how == "cross":
+            plx = self.__narwhals_namespace__()
+            key_token = generate_unique_token(
+                n_bytes=8, columns=[*self.columns, *other.columns]
+            )
 
-        if how == "left":  # type: ignore[comparison-overlap]
-            raise NotImplementedError
+            return self._from_native_dataframe(
+                self.with_columns(**{key_token: plx.lit(0, None)})._native_dataframe.join(
+                    other.with_columns(**{key_token: plx.lit(0, None)})._native_dataframe,
+                    keys=key_token,
+                    right_keys=key_token,
+                    join_type="inner",
+                    right_suffix="_right",
+                ),
+            ).drop(key_token)
 
         return self._from_native_dataframe(
             self._native_dataframe.join(
                 other._native_dataframe,
                 keys=left_on,
                 right_keys=right_on,
-                join_type=how,
+                join_type=how_to_join_map[how],
                 right_suffix="_right",
             ),
         )
diff --git a/narwhals/_arrow/expr.py b/narwhals/_arrow/expr.py
index d3e9ab056..ba00e34e0 100644
--- a/narwhals/_arrow/expr.py
+++ b/narwhals/_arrow/expr.py
@@ -215,6 +215,9 @@ def sample(
             self, "sample", n=n, fraction=fraction, with_replacement=with_replacement
         )
 
+    def fill_null(self: Self, value: Any) -> Self:
+        return reuse_series_implementation(self, "fill_null", value=value)
+
     @property
     def dt(self) -> ArrowExprDateTimeNamespace:
         return ArrowExprDateTimeNamespace(self)
diff --git a/narwhals/_arrow/series.py b/narwhals/_arrow/series.py
index 3e87d9ef9..f4080e489 100644
--- a/narwhals/_arrow/series.py
+++ b/narwhals/_arrow/series.py
@@ -320,6 +320,14 @@ def sample(
         mask = np.random.choice(idx, size=n, replace=with_replacement)
         return self._from_native_series(pc.take(ser, mask))
 
+    def fill_null(self: Self, value: Any) -> Self:
+        pa = get_pyarrow()
+        pc = get_pyarrow_compute()
+        ser = self._native_series
+        dtype = ser.type
+
+        return self._from_native_series(pc.fill_null(ser, pa.scalar(value, dtype)))
+
     @property
     def shape(self) -> tuple[int]:
         return (len(self._native_series),)
diff --git a/narwhals/_pandas_like/dataframe.py b/narwhals/_pandas_like/dataframe.py
index fa6e707ca..6606e8f15 100644
--- a/narwhals/_pandas_like/dataframe.py
+++ b/narwhals/_pandas_like/dataframe.py
@@ -13,7 +13,6 @@
 from narwhals._pandas_like.expr import PandasLikeExpr
 from narwhals._pandas_like.utils import Implementation
 from narwhals._pandas_like.utils import create_native_series
-from narwhals._pandas_like.utils import generate_unique_token
 from narwhals._pandas_like.utils import horizontal_concat
 from narwhals._pandas_like.utils import translate_dtype
 from narwhals._pandas_like.utils import validate_dataframe_comparand
@@ -23,6 +22,7 @@
 from narwhals.dependencies import get_numpy
 from narwhals.dependencies import get_pandas
 from narwhals.utils import flatten
+from narwhals.utils import generate_unique_token
 
 if TYPE_CHECKING:
     from typing_extensions import Self
diff --git a/narwhals/_pandas_like/utils.py b/narwhals/_pandas_like/utils.py
index 3548966ca..b493cfed2 100644
--- a/narwhals/_pandas_like/utils.py
+++ b/narwhals/_pandas_like/utils.py
@@ -1,6 +1,5 @@
 from __future__ import annotations
 
-import secrets
 from enum import Enum
 from enum import auto
 from typing import TYPE_CHECKING
@@ -458,31 +457,3 @@ def int_dtype_mapper(dtype: Any) -> str:
     if str(dtype).lower() != str(dtype):  # pragma: no cover
         return "Int64"
     return "int64"
-
-
-def generate_unique_token(n_bytes: int, columns: list[str]) -> str:  # pragma: no cover
-    """Generates a unique token of specified n_bytes that is not present in the given list of columns.
-
-    Arguments:
-        n_bytes : The number of bytes to generate for the token.
-        columns : The list of columns to check for uniqueness.
-
-    Returns:
-        A unique token that is not present in the given list of columns.
-
-    Raises:
-        AssertionError: If a unique token cannot be generated after 100 attempts.
-    """
-    counter = 0
-    while True:
-        token = secrets.token_hex(n_bytes)
-        if token not in columns:
-            return token
-
-        counter += 1
-        if counter > 100:
-            msg = (
-                "Internal Error: Narwhals was not able to generate a column name to perform cross "
-                "join operation"
-            )
-            raise AssertionError(msg)
diff --git a/narwhals/utils.py b/narwhals/utils.py
index 0edfe235d..c3ab3b060 100644
--- a/narwhals/utils.py
+++ b/narwhals/utils.py
@@ -1,6 +1,7 @@
 from __future__ import annotations
 
 import re
+import secrets
 from typing import TYPE_CHECKING
 from typing import Any
 from typing import Iterable
@@ -325,3 +326,31 @@ def is_ordered_categorical(series: Series) -> bool:
         return native_series.type.ordered  # type: ignore[no-any-return]
     # If it doesn't match any of the above, let's just play it safe and return False.
     return False  # pragma: no cover
+
+
+def generate_unique_token(n_bytes: int, columns: list[str]) -> str:  # pragma: no cover
+    """Generates a unique token of specified n_bytes that is not present in the given list of columns.
+
+    Arguments:
+        n_bytes : The number of bytes to generate for the token.
+        columns : The list of columns to check for uniqueness.
+
+    Returns:
+        A unique token that is not present in the given list of columns.
+
+    Raises:
+        AssertionError: If a unique token cannot be generated after 100 attempts.
+    """
+    counter = 0
+    while True:
+        token = secrets.token_hex(n_bytes)
+        if token not in columns:
+            return token
+
+        counter += 1
+        if counter > 100:
+            msg = (
+                "Internal Error: Narwhals was not able to generate a column name to perform given "
+                "join operation"
+            )
+            raise AssertionError(msg)
diff --git a/tests/expr_and_series/fill_null_test.py b/tests/expr_and_series/fill_null_test.py
index 5cffcddd7..dc9cc738e 100644
--- a/tests/expr_and_series/fill_null_test.py
+++ b/tests/expr_and_series/fill_null_test.py
@@ -1,7 +1,5 @@
 from typing import Any
 
-import pytest
-
 import narwhals.stable.v1 as nw
 from tests.utils import compare_dicts
 
@@ -12,10 +10,7 @@
 }
 
 
-def test_fill_null(request: Any, constructor: Any) -> None:
-    if "pyarrow_table" in str(constructor):
-        request.applymarker(pytest.mark.xfail)
-
+def test_fill_null(constructor: Any) -> None:
     df = nw.from_native(constructor(data), eager_only=True)
 
     result = df.with_columns(nw.col("a", "b", "c").fill_null(99))
diff --git a/tests/frame/join_test.py b/tests/frame/join_test.py
index 6264f8ea9..d8ab380c9 100644
--- a/tests/frame/join_test.py
+++ b/tests/frame/join_test.py
@@ -37,15 +37,11 @@ def test_inner_join_single_key(constructor: Any) -> None:
     compare_dicts(result, expected)
 
 
-def test_cross_join(request: Any, constructor: Any) -> None:
-    if "pyarrow_table" in str(constructor):
-        request.applymarker(pytest.mark.xfail)
-
+def test_cross_join(constructor: Any) -> None:
     data = {"a": [1, 3, 2]}
     df = nw.from_native(constructor(data))
-    result = df.join(df, how="cross")  # type: ignore[arg-type]
-
-    expected = {"a": [1, 1, 1, 3, 3, 3, 2, 2, 2], "a_right": [1, 3, 2, 1, 3, 2, 1, 3, 2]}
+    result = df.join(df, how="cross").sort("a", "a_right")  # type: ignore[arg-type]
+    expected = {"a": [1, 1, 1, 2, 2, 2, 3, 3, 3], "a_right": [1, 2, 3, 1, 2, 3, 1, 2, 3]}
     compare_dicts(result, expected)
 
     with pytest.raises(ValueError, match="Can not pass left_on, right_on for cross join"):
@@ -71,15 +67,11 @@ def test_cross_join_non_pandas() -> None:
     ],
 )
 def test_anti_join(
-    request: Any,
     constructor: Any,
     join_key: list[str],
     filter_expr: nw.Expr,
     expected: dict[str, list[Any]],
 ) -> None:
-    if "pyarrow_table" in str(constructor):
-        request.applymarker(pytest.mark.xfail)
-
     data = {"a": [1, 3, 2], "b": [4, 4, 6], "z": [7.0, 8, 9]}
     df = nw.from_native(constructor(data))
     other = df.filter(filter_expr)
@@ -96,15 +88,11 @@ def test_anti_join(
     ],
 )
 def test_semi_join(
-    request: Any,
     constructor: Any,
     join_key: list[str],
     filter_expr: nw.Expr,
     expected: dict[str, list[Any]],
 ) -> None:
-    if "pyarrow_table" in str(constructor):
-        request.applymarker(pytest.mark.xfail)
-
     data = {"a": [1, 3, 2], "b": [4, 4, 6], "z": [7.0, 8, 9]}
     df = nw.from_native(constructor(data))
     other = df.filter(filter_expr)
@@ -127,10 +115,7 @@ def test_join_not_implemented(constructor: Any, how: str) -> None:
 
 
 @pytest.mark.filterwarnings("ignore:the default coalesce behavior")
-def test_left_join(request: Any, constructor: Any) -> None:
-    if "pyarrow_table" in str(constructor):
-        request.applymarker(pytest.mark.xfail)
-
+def test_left_join(constructor: Any) -> None:
     data_left = {"a": [1.0, 2, 3], "b": [4.0, 5, 6]}
     data_right = {"a": [1.0, 2, 3], "c": [4.0, 5, 7]}
     df_left = nw.from_native(constructor(data_left), eager_only=True)
@@ -143,10 +128,7 @@ def test_left_join(request: Any, constructor: Any) -> None:
 
 
 @pytest.mark.filterwarnings("ignore: the default coalesce behavior")
-def test_left_join_multiple_column(request: Any, constructor: Any) -> None:
-    if "pyarrow_table" in str(constructor):
-        request.applymarker(pytest.mark.xfail)
-
+def test_left_join_multiple_column(constructor: Any) -> None:
     data_left = {"a": [1, 2, 3], "b": [4, 5, 6]}
     data_right = {"a": [1, 2, 3], "c": [4, 5, 6]}
     df_left = nw.from_native(constructor(data_left), eager_only=True)
@@ -157,12 +139,9 @@ def test_left_join_multiple_column(request: Any, constructor: Any) -> None:
 
 
 @pytest.mark.filterwarnings("ignore: the default coalesce behavior")
-def test_left_join_overlapping_column(request: Any, constructor: Any) -> None:
-    if "pyarrow_table" in str(constructor):
-        request.applymarker(pytest.mark.xfail)
-
-    data_left = {"a": [1, 2, 3], "b": [4, 5, 6], "d": [1, 4, 2]}
-    data_right = {"a": [1, 2, 3], "c": [4, 5, 6], "d": [1, 4, 2]}
+def test_left_join_overlapping_column(constructor: Any) -> None:
+    data_left = {"a": [1.0, 2, 3], "b": [4.0, 5, 6], "d": [1.0, 4, 2]}
+    data_right = {"a": [1.0, 2, 3], "c": [4.0, 5, 6], "d": [1.0, 4, 2]}
     df_left = nw.from_native(constructor(data_left), eager_only=True)
     df_right = nw.from_native(constructor(data_right), eager_only=True)
     result = df_left.join(df_right, left_on="b", right_on="c", how="left")
diff --git a/tests/hypothesis/test_join.py b/tests/hypothesis/test_join.py
index d5db53e3b..850caa1a3 100644
--- a/tests/hypothesis/test_join.py
+++ b/tests/hypothesis/test_join.py
@@ -2,6 +2,7 @@
 
 import pandas as pd
 import polars as pl
+import pyarrow as pa
 import pytest
 from hypothesis import assume
 from hypothesis import given
@@ -163,3 +164,18 @@ def test_left_join(  # pragma: no cover
         )
     ).select(pl.all().fill_null(float("nan")))
     compare_dicts(result_pd.to_dict(as_series=False), result_pl.to_dict(as_series=False))
+    # For PyArrow, insert an extra sort, as the order of rows isn't guaranteed
+    result_pa = (
+        nw.from_native(pa.table(data_left), eager_only=True)
+        .join(
+            nw.from_native(pa.table(data_right), eager_only=True),
+            how="left",
+            left_on=left_key,
+            right_on=right_key,
+        )
+        .select(nw.all().cast(nw.Float64).fill_null(float("nan")))
+        .pipe(lambda df: df.sort(df.columns))
+    )
+    compare_dicts(
+        result_pa, result_pd.pipe(lambda df: df.sort(df.columns)).to_dict(as_series=False)
+    )
diff --git a/utils/check_backend_completeness.py b/utils/check_backend_completeness.py
index 41466a15c..1c74f68ac 100644
--- a/utils/check_backend_completeness.py
+++ b/utils/check_backend_completeness.py
@@ -18,7 +18,6 @@
     "DataFrame.pipe",
     "DataFrame.unique",
     "Series.drop_nulls",
-    "Series.fill_null",
     "Series.from_iterable",
     "Series.is_between",
     "Series.is_duplicated",