diff --git a/ibis/backends/datafusion/__init__.py b/ibis/backends/datafusion/__init__.py
index 39549adfc50f..b9ac998532a2 100644
--- a/ibis/backends/datafusion/__init__.py
+++ b/ibis/backends/datafusion/__init__.py
@@ -12,6 +12,7 @@
 import sqlglot as sg
 from sqlglot import exp, transforms
 from sqlglot.dialects import Postgres
+from sqlglot.dialects.dialect import rename_func
 
 import ibis
 import ibis.common.exceptions as com
@@ -58,6 +59,7 @@ class Generator(Postgres.Generator):
                     transforms.eliminate_qualify,
                 ]
             ),
+            exp.IsNan: rename_func("isnan"),
         }
 
 
diff --git a/ibis/backends/datafusion/compiler/values.py b/ibis/backends/datafusion/compiler/values.py
index 0447e36da547..d59822fc0abd 100644
--- a/ibis/backends/datafusion/compiler/values.py
+++ b/ibis/backends/datafusion/compiler/values.py
@@ -1,6 +1,7 @@
 from __future__ import annotations
 
 import functools
+import math
 import operator
 from typing import Any
 
@@ -11,7 +12,6 @@
 import ibis.expr.operations as ops
 from ibis.backends.base.sqlglot import (
     NULL,
-    STAR,
     AggGen,
     F,
     interval,
@@ -202,6 +202,8 @@ def _literal(op, *, value, dtype, **kw):
     elif dtype.is_string() or dtype.is_macaddr():
         return sg.exp.convert(str(value))
     elif dtype.is_numeric():
+        if isinstance(value, float) and math.isinf(value):
+            return sg.exp.Literal.number("'+Inf'::double")
         return sg.exp.convert(value)
     elif dtype.is_interval():
         if dtype.unit.short in {"ms", "us", "ns"}:
@@ -324,7 +326,7 @@ def count_distinct(op, *, arg, where, **_):
 
 @translate_val.register(ops.CountStar)
 def count_star(op, *, where, **_):
-    return agg.count(STAR, where=where)
+    return agg.count(1, where=where)
 
 
 @translate_val.register(ops.Sum)
@@ -764,3 +766,13 @@ def correlation(op, *, left, right, where, **_):
         right = cast(right, dt.float64)
 
     return agg["corr"](left, right, where=where)
+
+
+@translate_val.register(ops.IsNull)
+def is_null(op, *, arg, **_):
+    return arg.is_(NULL)
+
+
+@translate_val.register(ops.IsNan)
+def is_nan(op, *, arg, **_):
+    return F.isnan(F.coalesce(arg, sg.exp.Literal.number("'NaN'::double")))
diff --git a/ibis/backends/tests/test_generic.py b/ibis/backends/tests/test_generic.py
index 08fad24d604f..fb2e99ca2993 100644
--- a/ibis/backends/tests/test_generic.py
+++ b/ibis/backends/tests/test_generic.py
@@ -128,13 +128,13 @@ def test_scalar_fillna_nullif(con, expr, expected):
         param(
             "nan_col",
             _.nan_col.isnan(),
-            marks=pytest.mark.notimpl(["datafusion", "mysql", "sqlite"]),
+            marks=pytest.mark.notimpl(["mysql", "sqlite"]),
             id="nan_col",
         ),
         param(
             "none_col",
             _.none_col.isnull(),
-            marks=[pytest.mark.notimpl(["datafusion", "mysql"])],
+            marks=[pytest.mark.notimpl(["mysql"])],
             id="none_col",
         ),
     ],
@@ -376,7 +376,7 @@ def test_case_where(backend, alltypes, df):
 
 
 # TODO: some of these are notimpl (datafusion) others are probably never
-@pytest.mark.notimpl(["datafusion", "mysql", "sqlite", "mssql", "druid", "oracle"])
+@pytest.mark.notimpl(["mysql", "sqlite", "mssql", "druid", "oracle"])
 @pytest.mark.notyet(["flink"], "NaN is not supported in Flink SQL", raises=ValueError)
 def test_select_filter_mutate(backend, alltypes, df):
     """Test that select, filter and mutate are executed in right order.
@@ -565,7 +565,6 @@ def test_order_by_random(alltypes):
     raises=sa.exc.ProgrammingError,
     reason="Druid only supports trivial unions",
 )
-@pytest.mark.notimpl(["datafusion"], raises=com.OperationNotDefinedError)
 def test_table_info(alltypes):
     expr = alltypes.info()
     df = expr.execute()
@@ -1372,11 +1371,6 @@ def test_try_cast_func(con, from_val, to_type, func):
                     raises=BadRequest,
                     reason="bigquery doesn't support OFFSET without LIMIT",
                 ),
-                pytest.mark.notyet(
-                    ["datafusion"],
-                    raises=AssertionError,
-                    reason="no support for offset yet",
-                ),
                 pytest.mark.notyet(
                     ["mssql"],
                     raises=sa.exc.CompileError,
@@ -1401,11 +1395,6 @@ def test_try_cast_func(con, from_val, to_type, func):
             lambda _: 1,
             id="[3:4]",
             marks=[
-                pytest.mark.notyet(
-                    ["datafusion"],
-                    raises=AssertionError,
-                    reason="no support for offset yet",
-                ),
                 pytest.mark.notyet(
                     ["mssql"],
                     raises=sa.exc.CompileError,
diff --git a/ibis/backends/tests/test_numeric.py b/ibis/backends/tests/test_numeric.py
index 3537a6a9080a..8fe6c8084b76 100644
--- a/ibis/backends/tests/test_numeric.py
+++ b/ibis/backends/tests/test_numeric.py
@@ -753,11 +753,17 @@ def test_decimal_literal(con, backend, expr, expected_types, expected_result):
             operator.methodcaller("isinf"),
             np.isinf,
             id="isinf",
+            marks=[
+                pytest.mark.notimpl(
+                    ["datafusion"],
+                    raises=com.OperationNotDefinedError,
+                )
+            ],
         ),
     ],
 )
 @pytest.mark.notimpl(
-    ["mysql", "sqlite", "datafusion", "mssql", "oracle", "flink"],
+    ["mysql", "sqlite", "mssql", "oracle", "flink"],
     raises=com.OperationNotDefinedError,
 )
 @pytest.mark.xfail(