Lots of attention and research activity has been devoted to partially hyperbolic dynamical systems and their perturbations in the past few decades; however, the main emphasis has been on features such as stable ergodicity and accessibility rather than stronger statistical properties such as existence of SRB measures and exponential decay of correlations. In fact, these properties have been previously proved under some specific conditions (e.g. Anosov flows, skew products) which, in particular, do not persist under perturbations. In this talk, we will construct an open (and thus stable for perturbations) class of partially hyperbolic smooth local diffeomorphisms of the two-torus which admit a unique SRB measure satisfying exponential decay of correlations for Hölder observables. This is joint work with C. Liverani.