In this talk I will first explain why second-order MFG with quadratic Hamiltonians and a variational structure can be written as entropy minimization problems. One advantage of this viewpoint is that it leads to fast numerical methods (joint work with J.-D. Benamou, L. Nenna and S. Di Marino). I will consider dynamic equilibrium city models which lead to new MFG models (leading to a system of four evolution PDES which are coupled at each time by an optimal transport like problem) for which the entropy viewpoint is particularly fruitful (joint work with César Barilla).