The theory of Mean Field Games has been recently proposed to model and analyze decision processes involving a very large number of indistinguishable rational agents. In this talk we consider both from the theoretical and numerical point of view some two-populations Mean Field Games systems with aversion between populations. We present in particular some results on existence, non-uniqueness of equilibria and segregation, which usually arises in this kind of models as individuals tend to avoid high distributions of players belonging to the other population. We explore numerically such segregation phenomena, both in the stationary (infinite-time horizon) and non-stationary (finite-time horizon) case using finite differences methods. Results are obtained in collaboration with M. Bardi and Y. Achdou.