diff --git a/dask_geopandas/backends.py b/dask_geopandas/backends.py
index b73559d..60408a1 100644
--- a/dask_geopandas/backends.py
+++ b/dask_geopandas/backends.py
@@ -1,6 +1,7 @@
 import uuid
 from packaging.version import Version
 
+import dask
 from dask import config
 
 # Check if dask-dataframe is using dask-expr (default of None means True as well)
@@ -84,3 +85,36 @@ def get_pyarrow_schema_geopandas(obj):
     for col in obj.columns[obj.dtypes == "geometry"]:
         df[col] = obj[col].to_wkb()
     return pa.Schema.from_pandas(df)
+
+
+if Version(dask.__version__) >= Version("2023.6.1"):
+    from dask.dataframe.dispatch import (
+        from_pyarrow_table_dispatch,
+        to_pyarrow_table_dispatch,
+    )
+
+    @to_pyarrow_table_dispatch.register((geopandas.GeoDataFrame,))
+    def get_pyarrow_table_from_geopandas(obj, **kwargs):
+        # `kwargs` must be supported by `pyarrow.Table.from_pandas`
+        import pyarrow as pa
+
+        if Version(geopandas.__version__).major < 1:
+            return pa.Table.from_pandas(obj.to_wkb(), **kwargs)
+        else:
+            # TODO handle kwargs?
+            return pa.table(obj.to_arrow())
+
+    @from_pyarrow_table_dispatch.register((geopandas.GeoDataFrame,))
+    def get_geopandas_geodataframe_from_pyarrow(meta, table, **kwargs):
+        # `kwargs` must be supported by `pyarrow.Table.to_pandas`
+        if Version(geopandas.__version__).major < 1:
+            df = table.to_pandas(**kwargs)
+
+            for col in meta.columns[meta.dtypes == "geometry"]:
+                df[col] = geopandas.GeoSeries.from_wkb(df[col], crs=meta[col].crs)
+
+            return df
+
+        else:
+            # TODO handle kwargs?
+            return geopandas.GeoDataFrame.from_arrow(table)
diff --git a/dask_geopandas/tests/test_distributed.py b/dask_geopandas/tests/test_distributed.py
new file mode 100644
index 0000000..9222df3
--- /dev/null
+++ b/dask_geopandas/tests/test_distributed.py
@@ -0,0 +1,38 @@
+from packaging.version import Version
+
+import geopandas
+
+import dask_geopandas
+
+import pytest
+from geopandas.testing import assert_geodataframe_equal
+
+distributed = pytest.importorskip("distributed")
+
+
+from distributed import Client, LocalCluster
+
+
+@pytest.mark.skipif(
+    Version(distributed.__version__) < Version("2024.6.0"),
+    reason="distributed < 2024.6 has a wrong assertion",
+    # https://github.com/dask/distributed/pull/8667
+)
+@pytest.mark.skipif(
+    Version(distributed.__version__) < Version("0.13"),
+    reason="geopandas < 0.13 does not implement sorting geometries",
+)
+def test_spatial_shuffle(naturalearth_cities):
+    df_points = geopandas.read_file(naturalearth_cities)
+
+    with LocalCluster(n_workers=1) as cluster:
+        with Client(cluster):
+            ddf_points = dask_geopandas.from_geopandas(df_points, npartitions=4)
+
+            ddf_result = ddf_points.spatial_shuffle(
+                by="hilbert", calculate_partitions=False
+            )
+            result = ddf_result.compute()
+
+    expected = df_points.sort_values("geometry").reset_index(drop=True)
+    assert_geodataframe_equal(result.reset_index(drop=True), expected)