Mean field games (MFGs) deal with the study and analysis of differential games (DGs) with a large number of indistinguishable, rational, and heterogeneous players. These methodologies approximate the Nash equilibriums for DGs with symmetric interactions among players. In contrast with classical game theory, MFGs model the interaction of a representative player with the collective behavior of the other players. In this talk, we discuss the basic concepts behind MFGs as well as their difference with classical game theory techniques. Moreover, we introduce analytic and probabilistic methods that solve for the Nash equilibrium of a MFG. Finally, we conclude with the many recent applications of MFGs in engineering such as future 5G networks, ultra dense networks, UAV networks, social networks, smart grid and security.