The billiard map of a polygonal billiard with the standard refection law is conservative and non-chaotic. Completely different dynamics arises when the reflection law is contracting, i.e. when the reflection angle measured from the normal is a contraction of the incidence angle. In this case, the billiard map is dissipative: the Liouville measure is no longer preserved. In this talk I will discuss recent results obtained in collaboration with Gianluigi Del Magno, João Lopes Dias and Pedro Duarte concerning the existence of SRB measures and their ergodic properties.