We review the present status of gauge theories built on various quantum
space-times described by noncommutative space-times. The mathematical tools and
notions underlying their construction are given. Different formulations of
gauge theory models on Moyal spaces as well as on quantum spaces whose
coordinates form a Lie algebra are covered, with particular emphasis on some
explored quantum properties. Recent attempts aiming to include gravity dynamics
within a noncommutative framework are also considered.
