We are going to present a PDE model that describe the evolution of a network of neurons that interact via their common statistical distribution. We will focus above all on qualitative and asymptotic properties of solutions describing convergence to a stationary state, blow up or synchronization phenomena. We will discuss the assumptions that are needed, on the coupling between the neurons and the intrinsic dynamic of neurons, to obtain complex patterns. This talk is based on collaborations with M. Caceres, J. A. Carrillo, B. Perthame, P. Roux, R. Schneider, D. Smets.