The theory of mean field type control aims at describing the behaviour of a large number of interacting agents using a common feedback. A phenomenon that have raised a lot of interest recently is called congestion: the agents try move while avoiding crowded regions. We will present a system of partial differential equations (PDE) arising in this setting: a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation describe respectively the evolution of the density of agents and of the value function. We are able to prove the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality. Based on this optimal control viewpoint, we develop an augmented Lagrangian algorithm solving numerically this mean field type control problem. This is joint work with Yves Achdou. Speaker(s): Matthieu Lauriere (NYU Shanghai)