diff --git a/test/test_scratch.py b/test/test_scratch.py
index 2b6673a31..df8c177f8 100755
--- a/test/test_scratch.py
+++ b/test/test_scratch.py
@@ -8,10 +8,11 @@
 """
 
 import pytest
+import warnings
 
 # This imports everything external code will see from ufl
 from ufl import *
-from ufl.log import error, warning
+from ufl.log import error
 from ufl.tensors import as_scalar, unit_indexed_tensor, unwrap_list_tensor
 
 # TODO: Import only what you need from classes and algorithms:
@@ -149,7 +150,7 @@ def compute_gprimeterm(ngrads, vval, vcomp, wshape, wcomp):
                 if self._cd._data:
                     # TODO: Make it possible to silence this message in particular?
                     #       It may be good to have for debugging...
-                    warning("Assuming d{%s}/d{%s} = 0." % (o, self._w))
+                    warnings.warn("Assuming d{%s}/d{%s} = 0." % (o, self._w))
             else:
                 # Make sure we have a tuple to match the self._v tuple
                 if not isinstance(oprimes, tuple):
diff --git a/ufl/__init__.py b/ufl/__init__.py
index 2132a5ae1..0517989fc 100644
--- a/ufl/__init__.py
+++ b/ufl/__init__.py
@@ -258,7 +258,7 @@
 
 # Output control
 from ufl.log import get_handler, get_logger, set_handler, set_level, add_logfile, \
-    UFLException, DEBUG, INFO, WARNING, ERROR, CRITICAL
+    UFLException, DEBUG, INFO, ERROR, CRITICAL
 
 # Types for geometric quantities
 
@@ -366,7 +366,7 @@
 __all__ = [
     'product',
     'get_handler', 'get_logger', 'set_handler', 'set_level', 'add_logfile',
-    'UFLException', 'DEBUG', 'INFO', 'WARNING', 'ERROR', 'CRITICAL',
+    'UFLException', 'DEBUG', 'INFO', 'ERROR', 'CRITICAL',
     'as_cell', 'AbstractCell', 'Cell', 'TensorProductCell',
     'as_domain', 'AbstractDomain', 'Mesh', 'MeshView', 'TensorProductMesh',
     'L2', 'H1', 'H2', 'HCurl', 'HDiv', 'HInf', 'HEin', 'HDivDiv',
diff --git a/ufl/algorithms/apply_derivatives.py b/ufl/algorithms/apply_derivatives.py
index c4123f3cc..ac94867ad 100644
--- a/ufl/algorithms/apply_derivatives.py
+++ b/ufl/algorithms/apply_derivatives.py
@@ -7,9 +7,10 @@
 #
 # SPDX-License-Identifier:    LGPL-3.0-or-later
 
+import warnings
 from collections import defaultdict
 
-from ufl.log import error, warning
+from ufl.log import error
 
 from ufl.core.expr import ufl_err_str
 from ufl.core.terminal import Terminal
@@ -1013,7 +1014,7 @@ def compute_gprimeterm(ngrads, vval, vcomp, wshape, wcomp):
                     # TODO: Make it possible to silence this message
                     #       in particular?  It may be good to have for
                     #       debugging...
-                    warning("Assuming d{%s}/d{%s} = 0." % (o, self._w))
+                    warnings.warn("Assuming d{%s}/d{%s} = 0." % (o, self._w))
             else:
                 # Make sure we have a tuple to match the self._v tuple
                 if not isinstance(oprimes, tuple):
diff --git a/ufl/algorithms/apply_geometry_lowering.py b/ufl/algorithms/apply_geometry_lowering.py
index 32c2ebae3..ef265f69d 100644
--- a/ufl/algorithms/apply_geometry_lowering.py
+++ b/ufl/algorithms/apply_geometry_lowering.py
@@ -11,10 +11,11 @@
 #
 # SPDX-License-Identifier:    LGPL-3.0-or-later
 
+import warnings
 from functools import reduce
 from itertools import combinations
 
-from ufl.log import error, warning
+from ufl.log import error
 
 from ufl.core.multiindex import Index, indices
 from ufl.corealg.multifunction import MultiFunction, memoized_handler
@@ -189,7 +190,7 @@ def cell_volume(self, o):
         if not domain.is_piecewise_linear_simplex_domain():
             # Don't lower for non-affine cells, instead leave it to
             # form compiler
-            warning("Only know how to compute the cell volume of an affine cell.")
+            warnings.warn("Only know how to compute the cell volume of an affine cell.")
             return o
 
         r = self.jacobian_determinant(JacobianDeterminant(domain))
@@ -206,7 +207,7 @@ def facet_area(self, o):
         if not domain.is_piecewise_linear_simplex_domain():
             # Don't lower for non-affine cells, instead leave it to
             # form compiler
-            warning("Only know how to compute the facet area of an affine cell.")
+            warnings.warn("Only know how to compute the facet area of an affine cell.")
             return o
 
         # Area of "facet" of interval (i.e. "area" of a vertex) is defined as 1.0
@@ -273,7 +274,7 @@ def _reduce_cell_edge_length(self, o, reduction_op):
 
         if not domain.ufl_coordinate_element().degree() == 1:
             # Don't lower bendy cells, instead leave it to form compiler
-            warning("Only know how to compute cell edge lengths of P1 or Q1 cell.")
+            warnings.warn("Only know how to compute cell edge lengths of P1 or Q1 cell.")
             return o
 
         elif domain.ufl_cell().cellname() == "interval":
@@ -297,7 +298,7 @@ def cell_diameter(self, o):
 
         if not domain.ufl_coordinate_element().degree() in {1, (1, 1)}:
             # Don't lower bendy cells, instead leave it to form compiler
-            warning("Only know how to compute cell diameter of P1 or Q1 cell.")
+            warnings.warn("Only know how to compute cell diameter of P1 or Q1 cell.")
             return o
 
         elif domain.is_piecewise_linear_simplex_domain():
@@ -331,7 +332,7 @@ def _reduce_facet_edge_length(self, o, reduction_op):
 
         elif not domain.ufl_coordinate_element().degree() == 1:
             # Don't lower bendy cells, instead leave it to form compiler
-            warning("Only know how to compute facet edge lengths of P1 or Q1 cell.")
+            warnings.warn("Only know how to compute facet edge lengths of P1 or Q1 cell.")
             return o
 
         else:
diff --git a/ufl/algorithms/estimate_degrees.py b/ufl/algorithms/estimate_degrees.py
index 115af6b48..6030909ac 100644
--- a/ufl/algorithms/estimate_degrees.py
+++ b/ufl/algorithms/estimate_degrees.py
@@ -10,7 +10,9 @@
 # Modified by Anders Logg, 2009-2010
 # Modified by Jan Blechta, 2012
 
-from ufl.log import warning, error
+import warnings
+
+from ufl.log import error
 from ufl.form import Form
 from ufl.integral import Integral
 from ufl.algorithms.multifunction import MultiFunction
@@ -117,7 +119,7 @@ def _not_handled(self, v, *args):
 
     def expr(self, v, *ops):
         "For most operators we take the max degree of its operands."
-        warning("Missing degree estimation handler for type %s" % v._ufl_class_.__name__)
+        warnings.warn("Missing degree estimation handler for type %s" % v._ufl_class_.__name__)
         return self._add_degrees(v, *ops)
 
     # Utility types with no degree concept
diff --git a/ufl/algorithms/formtransformations.py b/ufl/algorithms/formtransformations.py
index 984986de1..d11961ca3 100644
--- a/ufl/algorithms/formtransformations.py
+++ b/ufl/algorithms/formtransformations.py
@@ -12,8 +12,9 @@
 # Modified by Garth N. Wells, 2010.
 # Modified by Marie E. Rognes, 2010.
 
+import warnings
 
-from ufl.log import error, warning, debug
+from ufl.log import error, debug
 
 # All classes:
 from ufl.core.expr import ufl_err_str
@@ -316,7 +317,7 @@ def compute_form_with_arity(form, arity, arguments=None):
         error("compute_form_with_arity cannot handle parts.")
 
     if len(arguments) < arity:
-        warning("Form has no parts with arity %d." % arity)
+        warnings.warn("Form has no parts with arity %d." % arity)
         return 0 * form
 
     # Assuming that the form is not a sum of terms
diff --git a/ufl/conditional.py b/ufl/conditional.py
index b02761478..2cb8fab96 100644
--- a/ufl/conditional.py
+++ b/ufl/conditional.py
@@ -7,7 +7,9 @@
 #
 # SPDX-License-Identifier:    LGPL-3.0-or-later
 
-from ufl.log import warning, error
+import warnings
+
+from ufl.log import error
 from ufl.core.expr import ufl_err_str
 from ufl.core.ufl_type import ufl_type
 from ufl.core.operator import Operator
@@ -265,7 +267,7 @@ def evaluate(self, x, mapping, component, index_values):
         try:
             res = min(a, b)
         except ValueError:
-            warning('Value error in evaluation of min() of %s and %s.' % self.ufl_operands)
+            warnings.warn('Value error in evaluation of min() of %s and %s.' % self.ufl_operands)
             raise
         return res
 
@@ -290,7 +292,7 @@ def evaluate(self, x, mapping, component, index_values):
         try:
             res = max(a, b)
         except ValueError:
-            warning('Value error in evaluation of max() of %s and %s.' % self.ufl_operands)
+            warnings.warn('Value error in evaluation of max() of %s and %s.' % self.ufl_operands)
             raise
         return res
 
diff --git a/ufl/core/expr.py b/ufl/core/expr.py
index 97d8181b8..e6c355603 100644
--- a/ufl/core/expr.py
+++ b/ufl/core/expr.py
@@ -19,11 +19,13 @@
 # Modified by Anders Logg, 2008
 # Modified by Massimiliano Leoni, 2016
 
-from ufl.log import error, deprecate
+import warnings
 
+from ufl.log import error
 
 # --- The base object for all UFL expression tree nodes ---
 
+
 class Expr(object):
     """Base class for all UFL expression types.
 
@@ -293,15 +295,15 @@ def _ufl_expr_reconstruct_(self, *operands):
 
     def ufl_domains(self):
         "Return all domains this expression is defined on."
-        deprecate("Expr.ufl_domains() is deprecated, please "
-                  "use extract_domains(expr) instead.")
+        warnings.warn("Expr.ufl_domains() is deprecated, please "
+                      "use extract_domains(expr) instead.", DeprecationWarning)
         from ufl.domain import extract_domains
         return extract_domains(self)
 
     def ufl_domain(self):
         "Return the single unique domain this expression is defined on, or throw an error."
-        deprecate("Expr.ufl_domain() is deprecated, please "
-                  "use extract_unique_domain(expr) instead.")
+        warnings.warn("Expr.ufl_domain() is deprecated, please "
+                      "use extract_unique_domain(expr) instead.", DeprecationWarning)
         from ufl.domain import extract_unique_domain
         return extract_unique_domain(self)
 
diff --git a/ufl/core/terminal.py b/ufl/core/terminal.py
index 490bdbeba..5b0840268 100644
--- a/ufl/core/terminal.py
+++ b/ufl/core/terminal.py
@@ -11,7 +11,9 @@
 # Modified by Anders Logg, 2008
 # Modified by Massimiliano Leoni, 2016
 
-from ufl.log import error, warning
+import warnings
+
+from ufl.log import error
 from ufl.core.expr import Expr
 from ufl.core.ufl_type import ufl_type
 
@@ -59,7 +61,7 @@ def evaluate(self, x, mapping, component, index_values, derivatives=()):
             if hasattr(self, 'ufl_evaluate'):
                 return self.ufl_evaluate(x, component, derivatives)
             # Take component if any
-            warning("Couldn't map '%s' to a float, returning ufl object without evaluation." % str(self))
+            warnings.warn("Couldn't map '%s' to a float, returning ufl object without evaluation." % str(self))
             f = self
             if component:
                 f = f[component]
diff --git a/ufl/finiteelement/elementlist.py b/ufl/finiteelement/elementlist.py
index e45fc7813..f5ed2265b 100644
--- a/ufl/finiteelement/elementlist.py
+++ b/ufl/finiteelement/elementlist.py
@@ -13,9 +13,10 @@
 # Modified by Lizao Li <lzlarryli@gmail.com>, 2015, 2016
 # Modified by Massimiliano Leoni, 2016
 
+import warnings
 from numpy import asarray
 
-from ufl.log import warning, error
+from ufl.log import error
 from ufl.sobolevspace import L2, H1, H2, HDiv, HCurl, HEin, HDivDiv, HInf
 from ufl.utils.formatting import istr
 from ufl.cell import Cell, TensorProductCell
@@ -436,11 +437,11 @@ def canonical_element_description(family, cell, order, form_degree):
             family = "Q"
         elif family == "Discontinuous Lagrange":
             if order >= 1:
-                warning("Discontinuous Lagrange element requested on %s, creating DQ element." % cell.cellname())
+                warnings.warn("Discontinuous Lagrange element requested on %s, creating DQ element." % cell.cellname())
             family = "DQ"
         elif family == "Discontinuous Lagrange L2":
             if order >= 1:
-                warning("Discontinuous Lagrange L2 element requested on %s, creating DQ L2 element." % cell.cellname())
+                warnings.warn("Discontinuous Lagrange L2 element requested on %s, creating DQ L2 element." % cell.cellname())
             family = "DQ L2"
 
     # Validate cellname if a valid cell is specified
diff --git a/ufl/form.py b/ufl/form.py
index 52ea2680e..838a93a1b 100644
--- a/ufl/form.py
+++ b/ufl/form.py
@@ -11,10 +11,11 @@
 # Modified by Massimiliano Leoni, 2016.
 # Modified by Cecile Daversin-Catty, 2018.
 
+import warnings
 from itertools import chain
 from collections import defaultdict
 
-from ufl.log import error, warning
+from ufl.log import error
 from ufl.domain import sort_domains
 from ufl.integral import Integral
 from ufl.checks import is_scalar_constant_expression
@@ -378,7 +379,7 @@ def __call__(self, *args, **kwargs):
                 if f in coeffs:
                     repdict[f] = coefficients[f]
                 else:
-                    warning("Coefficient %s is not in form." % ufl_err_str(f))
+                    warnings.warn("Coefficient %s is not in form." % ufl_err_str(f))
         if repdict:
             from ufl.formoperators import replace
             return replace(self, repdict)
diff --git a/ufl/log.py b/ufl/log.py
index 7a7da9e4b..3379e8741 100644
--- a/ufl/log.py
+++ b/ufl/log.py
@@ -14,22 +14,19 @@
 import sys
 import types
 import logging
-from logging import DEBUG, INFO, WARNING, ERROR, CRITICAL  # noqa: F401
+import warnings
+from logging import DEBUG, INFO, ERROR, CRITICAL  # noqa: F401
 
-log_functions = ["log", "debug", "info", "deprecate", "warning", "error",
+log_functions = ["log", "debug", "info", "error",
                  "begin", "end",
                  "set_level", "push_level", "pop_level", "set_indent",
                  "add_indent",
                  "set_handler", "get_handler", "get_logger", "add_logfile",
                  "set_prefix",
-                 "info_red", "info_green", "info_blue",
-                 "warning_red", "warning_green", "warning_blue"]
+                 "info_red", "info_green", "info_blue"]
 
 __all__ = log_functions + ["Logger", "log_functions"] +\
-    ["DEBUG", "INFO", "DEPRECATE", "WARNING", "ERROR", "CRITICAL"]
-
-
-DEPRECATE = (INFO + WARNING) // 2
+    ["DEBUG", "INFO", "ERROR", "CRITICAL"]
 
 
 # This is used to override emit() in StreamHandler for printing
@@ -63,7 +60,7 @@ def __init__(self, name, exception_type=Exception):
 
         # Set up handler
         h = logging.StreamHandler(sys.stdout)
-        h.setLevel(WARNING)
+        h.setLevel(ERROR)
         # Override emit() in handler for indentation
         h.emit = types.MethodType(emit, h)
         self._handler = h
@@ -90,7 +87,7 @@ def add_logfile(self, filename=None, mode="a", level=DEBUG):
         if filename is None:
             filename = "%s.log" % self._name
         if filename in self._logfiles:
-            self.warning("Adding logfile %s multiple times." % filename)
+            warnings.warn("Adding logfile %s multiple times." % filename)
             return
         h = logging.FileHandler(filename, mode)
         h.emit = types.MethodType(emit, h)
@@ -132,26 +129,6 @@ def info_blue(self, *message):
         "Write info message in blue."
         self.log(INFO, BLUE % self._format_raw(*message))
 
-    def deprecate(self, *message):
-        "Write deprecation message."
-        self.log(DEPRECATE, RED % self._format_raw(*message))
-
-    def warning(self, *message):
-        "Write warning message."
-        self._log.warning(self._format(*message))
-
-    def warning_red(self, *message):
-        "Write warning message in red."
-        self._log.warning(RED % self._format(*message))
-
-    def warning_green(self, *message):
-        "Write warning message in green."
-        self._log.warning(GREEN % self._format(*message))
-
-    def warning_blue(self, *message):
-        "Write warning message in blue."
-        self._log.warning(BLUE % self._format(*message))
-
     def error(self, *message):
         "Write error message and raise an exception."
         self._log.error(*message)
@@ -242,4 +219,4 @@ class UFLValueError(UFLException):
 for foo in log_functions:
     exec("%s = ufl_logger.%s" % (foo, foo))
 
-set_level(DEPRECATE)  # noqa
+set_level(ERROR)  # noqa
diff --git a/ufl/mathfunctions.py b/ufl/mathfunctions.py
index 3d3c877c0..a53ff4e91 100644
--- a/ufl/mathfunctions.py
+++ b/ufl/mathfunctions.py
@@ -13,8 +13,9 @@
 import math
 import cmath
 import numbers
+import warnings
 
-from ufl.log import warning, error
+from ufl.log import error
 from ufl.core.operator import Operator
 from ufl.core.ufl_type import ufl_type
 from ufl.constantvalue import is_true_ufl_scalar, Zero, RealValue, FloatValue, IntValue, ComplexValue, ConstantValue, as_ufl
@@ -63,7 +64,7 @@ def evaluate(self, x, mapping, component, index_values):
             else:
                 res = getattr(cmath, self._name)(a)
         except ValueError:
-            warning('Value error in evaluation of function %s with argument %s.' % (self._name, a))
+            warnings.warn('Value error in evaluation of function %s with argument %s.' % (self._name, a))
             raise
         return res
 
@@ -289,7 +290,7 @@ def evaluate(self, x, mapping, component, index_values):
         except TypeError:
             error('Atan2 does not support complex numbers.')
         except ValueError:
-            warning('Value error in evaluation of function atan_2 with arguments %s, %s.' % (a, b))
+            warnings.warn('Value error in evaluation of function atan_2 with arguments %s, %s.' % (a, b))
             raise
         return res
 
diff --git a/ufl/operators.py b/ufl/operators.py
index 256beaa84..786561289 100644
--- a/ufl/operators.py
+++ b/ufl/operators.py
@@ -13,9 +13,10 @@
 # Modified by Kristian B. Oelgaard, 2011
 # Modified by Massimiliano Leoni, 2016.
 
+import warnings
 import operator
 
-from ufl.log import error, warning
+from ufl.log import error
 from ufl.form import Form
 from ufl.constantvalue import Zero, RealValue, ComplexValue, as_ufl
 from ufl.differentiation import VariableDerivative, Grad, Div, Curl, NablaGrad, NablaDiv
@@ -450,7 +451,7 @@ def jump(v, n=None):
         else:
             return dot(v('+'), n('+')) + dot(v('-'), n('-'))
     else:
-        warning("Returning zero from jump of expression without a domain. This may be erroneous if a dolfin.Expression is involved.")
+        warnings.warn("Returning zero from jump of expression without a domain. This may be erroneous if a dolfin.Expression is involved.")
         # FIXME: Is this right? If v has no domain, it doesn't depend
         # on anything spatially variable or any form arguments, and
         # thus the jump is zero. In other words, I'm assuming that "v
diff --git a/ufl/precedence.py b/ufl/precedence.py
index b5ca6c052..aee5c1537 100644
--- a/ufl/precedence.py
+++ b/ufl/precedence.py
@@ -7,7 +7,7 @@
 #
 # SPDX-License-Identifier:    LGPL-3.0-or-later
 
-from ufl.log import warning
+import warnings
 
 
 # FIXME: This code is crap...
@@ -102,7 +102,7 @@ def assign_precedences(precedence_list):
     if missing:
         msg = "Missing precedence levels for classes:\n" +\
             "\n".join('  %s' % c for c in sorted(missing))
-        warning(msg)
+        warnings.warn(msg)
 
 
 """
diff --git a/ufl/utils/sorting.py b/ufl/utils/sorting.py
index fe73fe890..14cb9e33c 100644
--- a/ufl/utils/sorting.py
+++ b/ufl/utils/sorting.py
@@ -7,7 +7,7 @@
 #
 # SPDX-License-Identifier:    LGPL-3.0-or-later
 
-from ufl.log import warning
+import warnings
 
 
 def topological_sorting(nodes, edges):
@@ -91,7 +91,7 @@ def canonicalize_metadata(metadata):
         elif isinstance(value, (int, float, str)) or value is None:
             value = str(value)
         else:
-            warning("Applying str() to a metadata value of type {0}, don't know if this is safe.".format(type(value).__name__))
+            warnings.warn("Applying str() to a metadata value of type {0}, don't know if this is safe.".format(type(value).__name__))
             value = str(value)
         newvalues.append(value)