diff --git a/conan/tools/cmake/cmake.py b/conan/tools/cmake/cmake.py
index b4a2098a6f7..270c0c123f0 100644
--- a/conan/tools/cmake/cmake.py
+++ b/conan/tools/cmake/cmake.py
@@ -60,7 +60,7 @@ def __init__(self, conanfile, namespace=None):
 
         self._cmake_program = "cmake"  # Path to CMake should be handled by environment
 
-    def configure(self, build_script_folder=None):
+    def configure(self, variables=None, build_script_folder=None):
         cmakelist_folder = self._conanfile.source_folder
         if build_script_folder:
             cmakelist_folder = os.path.join(self._conanfile.source_folder, build_script_folder)
@@ -83,7 +83,10 @@ def configure(self, build_script_folder=None):
             pkg_folder = self._conanfile.package_folder.replace("\\", "/")
             arg_list.append('-DCMAKE_INSTALL_PREFIX="{}"'.format(pkg_folder))
         if platform.system() == "Windows" and self._generator == "MinGW Makefiles":
+            # It seems this doesn't work in the toolchain file, it needs to be here in command line
             arg_list.append('-DCMAKE_SH="CMAKE_SH-NOTFOUND"')
+        if variables:
+            arg_list.extend(["-D{}={}".format(k, v) for k, v in variables.items()])
         arg_list.append('"{}"'.format(cmakelist_folder))
 
         command = " ".join(arg_list)
@@ -91,7 +94,7 @@ def configure(self, build_script_folder=None):
         with chdir(self, build_folder):
             self._conanfile.run(command)
 
-    def _build(self, build_type=None, target=None):
+    def _build(self, build_type=None, target=None, cli_args=None, build_tool_args=None):
         bf = self._conanfile.build_folder
         is_multi = is_multi_configuration(self._generator)
         if build_type and not is_multi:
@@ -106,8 +109,12 @@ def _build(self, build_type=None, target=None):
         args = []
         if target is not None:
             args = ["--target", target]
+        if cli_args:
+            args.extend(cli_args)
 
         cmd_line_args = _cmake_cmd_line_args(self._conanfile, self._generator)
+        if build_tool_args:
+            cmd_line_args.extend(build_tool_args)
         if cmd_line_args:
             args += ['--'] + cmd_line_args
 
@@ -117,8 +124,8 @@ def _build(self, build_type=None, target=None):
         self._conanfile.output.info("CMake command: %s" % command)
         self._conanfile.run(command)
 
-    def build(self, build_type=None, target=None):
-        self._build(build_type, target)
+    def build(self, build_type=None, target=None, cli_args=None, build_tool_args=None):
+        self._build(build_type, target, cli_args, build_tool_args)
 
     def install(self, build_type=None):
         mkdir(self._conanfile, self._conanfile.package_folder)
@@ -137,11 +144,12 @@ def install(self, build_type=None):
         self._conanfile.output.info("CMake command: %s" % command)
         self._conanfile.run(command)
 
-    def test(self, build_type=None, target=None, output_on_failure=False):
+    def test(self, build_type=None, target=None, cli_args=None, build_tool_args=None):
         if self._conanfile.conf["tools.build:skip_test"]:
             return
         if not target:
             is_multi = is_multi_configuration(self._generator)
             target = "RUN_TESTS" if is_multi else "test"
 
-        self._build(build_type=build_type, target=target)
+        self._build(build_type=build_type, target=target, cli_args=cli_args,
+                    build_tool_args=build_tool_args)
diff --git a/conans/test/integration/toolchains/cmake/test_cmake.py b/conans/test/integration/toolchains/cmake/test_cmake.py
new file mode 100644
index 00000000000..7687b6783b5
--- /dev/null
+++ b/conans/test/integration/toolchains/cmake/test_cmake.py
@@ -0,0 +1,34 @@
+import textwrap
+
+from conans.test.utils.tools import TestClient
+
+
+def test_configure_args():
+    client = TestClient()
+
+    conanfile = textwrap.dedent("""
+        from conan import ConanFile
+        from conan.tools.cmake import CMake
+        class Pkg(ConanFile):
+            name = "pkg"
+            version = "0.1"
+            settings = "os", "compiler", "build_type", "arch"
+            generators = "CMakeToolchain"
+            def build(self):
+                cmake = CMake(self)
+                cmake.configure(variables={"MYVAR": "MYVALUE"})
+                cmake.build(cli_args=["--verbosebuild"], build_tool_args=["-something"])
+                cmake.test(cli_args=["--testverbose"], build_tool_args=["-testok"])
+
+            def run(self, *args, **kwargs):
+                self.output.info("MYRUN: {}".format(*args))
+            """)
+    client.save({"conanfile.py": conanfile})
+    client.run("create . ")
+    # TODO: This check is ugly, because the command line is so different in each platform,
+    #  and args_to_string() is doing crazy stuff
+    assert '-DMYVAR=MYVALUE' in client.out
+    assert "--verbosebuild" in client.out
+    assert "-something" in client.out
+    assert "--testverbose" in client.out
+    assert "-testok" in client.out