A large variety of complex systems, from the brain to the weather networks and complex infrastructures, are formed by several networks that coexist, interact and coevolve forming a “network of networks”. Modeling such multilayer structures and characterizing  the rich interplay between their structure and their dynamical behavior is crucial in order to understand and predict complex phenomena. In this talk I will present recent works on statistical mechanics of  multiplex networks. Multiplex networks are  formed by N nodes linked in different layers by different networks. I will present models that generate multiplexes with different types of correlations between the layers, and characterize new percolation phenomena on multiplex networks, showing first order phase transitions,   bistability or a complex phase diagram with tricriticals points and higher order critical points.