  We give a pedagogical account of noncommutative gauge and gravity theories,
where the exterior product between forms is deformed into a $\star$-product via
an abelian twist (e.g. the Groenewold-Moyal twist). The Seiberg-Witten map
between commutative and noncommutative gauge theories is introduced. It allows
to express the action of noncommutative Einstein gravity coupled to spinor
fields in terms of the usual commutative action with commutative fields plus
extra interaction terms dependent on the noncommutativity parameter.
