diff --git a/doc/source/whatsnew/v0.25.2.rst b/doc/source/whatsnew/v0.25.2.rst
index 76473405374e8..403c02c3ff129 100644
--- a/doc/source/whatsnew/v0.25.2.rst
+++ b/doc/source/whatsnew/v0.25.2.rst
@@ -99,7 +99,7 @@ Sparse
 Other
 ^^^^^
 
--
+- Compatibility with Python 3.8 in :meth:`DataFrame.query` (:issue:`27261`)
 -
 
 .. _whatsnew_0.252.contributors:
diff --git a/pandas/compat/__init__.py b/pandas/compat/__init__.py
index b32da8da3a1fb..9c778f68727c6 100644
--- a/pandas/compat/__init__.py
+++ b/pandas/compat/__init__.py
@@ -15,6 +15,7 @@
 PY35 = sys.version_info[:2] == (3, 5)
 PY36 = sys.version_info >= (3, 6)
 PY37 = sys.version_info >= (3, 7)
+PY38 = sys.version_info >= (3, 8)
 PYPY = platform.python_implementation() == "PyPy"
 
 
diff --git a/pandas/core/computation/expr.py b/pandas/core/computation/expr.py
index a58f256cf61d4..4c164968575a1 100644
--- a/pandas/core/computation/expr.py
+++ b/pandas/core/computation/expr.py
@@ -582,6 +582,9 @@ def visit_NameConstant(self, node, **kwargs):
     def visit_Num(self, node, **kwargs):
         return self.const_type(node.n, self.env)
 
+    def visit_Constant(self, node, **kwargs):
+        return self.const_type(node.n, self.env)
+
     def visit_Str(self, node, **kwargs):
         name = self.env.add_tmp(node.s)
         return self.term_type(name, self.env)
diff --git a/pandas/tests/computation/test_eval.py b/pandas/tests/computation/test_eval.py
index c500760fa1390..b6ffd8a83e409 100644
--- a/pandas/tests/computation/test_eval.py
+++ b/pandas/tests/computation/test_eval.py
@@ -14,7 +14,7 @@
 from pandas.core.dtypes.common import is_bool, is_list_like, is_scalar
 
 import pandas as pd
-from pandas import DataFrame, Series, date_range
+from pandas import DataFrame, Series, compat, date_range
 from pandas.core.computation import pytables
 from pandas.core.computation.check import _NUMEXPR_VERSION
 from pandas.core.computation.engines import NumExprClobberingError, _engines
@@ -1267,7 +1267,10 @@ def test_assignment_column(self):
         msg = "left hand side of an assignment must be a single name"
         with pytest.raises(SyntaxError, match=msg):
             df.eval("d,c = a + b")
-        msg = "can't assign to function call"
+        if compat.PY38:
+            msg = "cannot assign to function call"
+        else:
+            msg = "can't assign to function call"
         with pytest.raises(SyntaxError, match=msg):
             df.eval('Timestamp("20131001") = a + b')
 
@@ -1967,6 +1970,26 @@ def test_bool_ops_fails_on_scalars(lhs, cmp, rhs, engine, parser):
             pd.eval(ex, engine=engine, parser=parser)
 
 
+@pytest.mark.parametrize(
+    "other",
+    [
+        "'x'",
+        pytest.param(
+            "...", marks=pytest.mark.xfail(not compat.PY38, reason="GH-28116")
+        ),
+    ],
+)
+def test_equals_various(other):
+    df = DataFrame({"A": ["a", "b", "c"]})
+    result = df.eval("A == {}".format(other))
+    expected = Series([False, False, False], name="A")
+    if _USE_NUMEXPR:
+        # https://github.com/pandas-dev/pandas/issues/10239
+        # lose name with numexpr engine. Remove when that's fixed.
+        expected.name = None
+    tm.assert_series_equal(result, expected)
+
+
 def test_inf(engine, parser):
     s = "inf + 1"
     expected = np.inf
diff --git a/pandas/tests/io/parser/test_common.py b/pandas/tests/io/parser/test_common.py
index e5366a8357adb..e04535df56663 100644
--- a/pandas/tests/io/parser/test_common.py
+++ b/pandas/tests/io/parser/test_common.py
@@ -1898,7 +1898,10 @@ def test_null_byte_char(all_parsers):
         out = parser.read_csv(StringIO(data), names=names)
         tm.assert_frame_equal(out, expected)
     else:
-        msg = "NULL byte detected"
+        if compat.PY38:
+            msg = "line contains NUL"
+        else:
+            msg = "NULL byte detected"
         with pytest.raises(ParserError, match=msg):
             parser.read_csv(StringIO(data), names=names)
 
diff --git a/pandas/tests/scalar/test_nat.py b/pandas/tests/scalar/test_nat.py
index 5b1c4f92bf341..5eb69fb2952dc 100644
--- a/pandas/tests/scalar/test_nat.py
+++ b/pandas/tests/scalar/test_nat.py
@@ -252,6 +252,7 @@ def _get_overlap_public_nat_methods(klass, as_tuple=False):
                 "day_name",
                 "dst",
                 "floor",
+                "fromisocalendar",
                 "fromisoformat",
                 "fromordinal",
                 "fromtimestamp",
@@ -296,6 +297,8 @@ def test_overlap_public_nat_methods(klass, expected):
     # "fromisoformat" was introduced in 3.7
     if klass is Timestamp and not compat.PY37:
         expected.remove("fromisoformat")
+    if klass is Timestamp and not compat.PY38:
+        expected.remove("fromisocalendar")
 
     assert _get_overlap_public_nat_methods(klass) == expected