I will introduce the basic features of the probabilistic approach to mean field games, based on forward-backward stochastic differential equations of the McKean Vlasov type. I will insist first on the main tools that may be used to tackle such types of systems. Meanwhile, I will also discuss examples when uniqueness holds true. In a second step, I will address mean field games with a common noise and explain how to adapt the analysis of the corresponding forward-backward system. Last, I will make the connection with the so-called master equation for mean field games, as introduced by Lions in his lectures at Collège de France. I will exemplify the interest of this master equation in the analysis of the convergence problem for MFG. Most of the materials for my talk will be based on a book, under press (Springer editions), written in collaboration with René Carmona.