In the last three decades several works have been done on the stable ergodicity problem. Almost every work that exists was done in the partially hyperbolic setting. The only result about stable ergodicity outside the partially hyperbolic world was done by Tahzibi in 2004, where he gives examples of stably ergodic diffeomorphisms which are not partially hyperbolic. In this seminar I will talk about a criterium of stable ergodicity for diffeomorphisms with dominated splitting and some applications of this criterium.