I will discuss some results on the long time behaviour in Mean Field Games, first under the assumption that the coupling is mildly nonmonotone in the usual Lasry-Lions sense, then in the displacement monotone setting. Finally, I will present recent results on the local uniqueness of solutions to an infinite horizon mean field game inspired by the Kuramoto model.Based on joint works with A. Cesaroni, A. Porretta and A. R. Meszaros.