diff --git a/CMakeLists.txt b/CMakeLists.txt
index 63da430d..551c11b7 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -172,9 +172,42 @@ if(WANT_PERL)
 endif()
 if (WANT_PYTHON)
 	find_package(Perl 5.10 REQUIRED)
-	pkg_check_modules(PYTHON "${WANT_PYTHON_VERSION}-embed")
-	if (NOT PYTHON_FOUND)
-		pkg_check_modules(PYTHON "${WANT_PYTHON_VERSION}" REQUIRED)
+	# VERSION_GREATER_EQUAL is available only since 3.7
+	if (CMAKE_VERSION VERSION_LESS 3.12)
+	else()
+		# Even if FindPython3 is available (since CMake 3.12) we still use
+		# pkg-config, because FindPython has a hardcoded list of python
+		# versions, which may become outdated when new pythons are released,
+		# but when cmake in the distro is old.
+		#
+		# Why FindPython3 is useful at all? Because sometimes there is no
+		# python3.pc, but only python-3.5.pc and python-3.6.pc; which would
+		# force user to provide the version explicitly via
+		# WANT_PYTHON_VERSION. This is the case on Gentoo when NOT building
+		# via emerge.
+		if (WANT_PYTHON_VERSION STREQUAL "python3")
+			find_package(Python3 COMPONENTS Development)
+		else()
+			# We used to pass value like "python-3.5" to the variable.
+			if (WANT_PYTHON_VERSION MATCHES "^(python-)?(.*)$")
+				find_package(Python3 COMPONENTS Development
+					EXACT "${CMAKE_MATCH_2}")
+			else()
+				message(FATAL_ERROR "Invalid value of WANT_PYTHON_VERSION")
+			endif()
+		endif()
+		# Compatibility with pkg-config variables
+		set(Python3_LDFLAGS "${Python3_LIBRARIES}")
+	endif()
+	if (NOT Python3_FOUND AND WANT_PYTHON_VERSION MATCHES "^python")
+		# Since python 3.8, -embed is required for embedding.
+		pkg_check_modules(Python3 "${WANT_PYTHON_VERSION}-embed >= 3.0")
+		if (NOT Python3_FOUND)
+			pkg_check_modules(Python3 "${WANT_PYTHON_VERSION} >= 3.0")
+		endif()
+	endif()
+	if (NOT Python3_FOUND)
+		message(FATAL_ERROR "Python 3 is not found. Try disabling it.")
 	endif()
 endif()
 
@@ -361,7 +394,7 @@ summary_line("SSL      " "${OPENSSL_FOUND}")
 summary_line("IPv6     " "${WANT_IPV6}")
 summary_line("Async DNS" "${HAVE_THREADED_DNS}")
 summary_line("Perl     " "${PERLLIBS_FOUND}")
-summary_line("Python   " "${PYTHON_FOUND}")
+summary_line("Python   " "${Python3_FOUND}")
 summary_line("Tcl      " "${TCL_FOUND}")
 summary_line("Cyrus    " "${CYRUS_FOUND}")
 summary_line("Charset  " "${ICU_FOUND}")
diff --git a/cmake/use_homebrew.cmake b/cmake/use_homebrew.cmake
index f58c1542..bb59317b 100644
--- a/cmake/use_homebrew.cmake
+++ b/cmake/use_homebrew.cmake
@@ -50,7 +50,7 @@ execute_process(COMMAND "${brew}" --prefix python3
 if(brew_python_f EQUAL 0)
 	find_package_message(brew_python "Python via Homebrew: ${brew_python}"
 		"${brew_python}")
-	list(APPEND Python_FRAMEWORKS_ADDITIONAL
+	list(APPEND Python3_FRAMEWORKS_ADDITIONAL
 		"${brew_python}/Frameworks/Python.framework")
 endif()
 
diff --git a/modules/CMakeLists.txt b/modules/CMakeLists.txt
index 50921c7b..7f4d6b57 100644
--- a/modules/CMakeLists.txt
+++ b/modules/CMakeLists.txt
@@ -66,7 +66,7 @@ else()
 	set(moddisable_modperl true)
 endif()
 
-if(PYTHON_FOUND)
+if(Python3_FOUND)
 	add_subdirectory(modpython)
 else()
 	set(moddisable_modpython true)
diff --git a/modules/modpython/CMakeLists.txt b/modules/modpython/CMakeLists.txt
index 3a59ed75..ed715eda 100644
--- a/modules/modpython/CMakeLists.txt
+++ b/modules/modpython/CMakeLists.txt
@@ -17,9 +17,9 @@
 # TODO: consider switching to swig_add_library() after bumping CMake
 # requirements to 3.8, when that command started using IMPLICIT_DEPENDS
 
-set(modinclude_modpython PUBLIC ${PYTHON_INCLUDE_DIRS}
+set(modinclude_modpython PUBLIC ${Python3_INCLUDE_DIRS}
 	"${CMAKE_CURRENT_BINARY_DIR}/.." PARENT_SCOPE)
-set(modlink_modpython PUBLIC ${PYTHON_LDFLAGS} PARENT_SCOPE)
+set(modlink_modpython PUBLIC ${Python3_LDFLAGS} PARENT_SCOPE)
 set(moddef_modpython PUBLIC "SWIG_TYPE_TABLE=znc" PARENT_SCOPE)
 set(moddepend_modpython modpython_functions modpython_swigruntime PARENT_SCOPE)
 
@@ -75,8 +75,8 @@ target_include_directories(modpython_lib PRIVATE
 	"${PROJECT_SOURCE_DIR}/include"
 	"${CMAKE_CURRENT_BINARY_DIR}/.."
 	"${CMAKE_CURRENT_SOURCE_DIR}/.."
-	${PYTHON_INCLUDE_DIRS})
-target_link_libraries(modpython_lib ${znc_link} ${PYTHON_LDFLAGS})
+	${Python3_INCLUDE_DIRS})
+target_link_libraries(modpython_lib ${znc_link} ${Python3_LDFLAGS})
 set_target_properties(modpython_lib PROPERTIES
 	PREFIX "_"
 	OUTPUT_NAME "znc_core"