PDEs with oscillatory coefficients arise in many applications, such as the modeling of composite materials and flame propagations. The fine scale oscillations of the physical media are often unknown and, hence, modeled as random. The theory of stochastic homogenization amounts to exploring the self-averaging mechanism of the PDEs, and it leads to mean field approximations of large scale behaviors of the solution. In this talk, I will present the classical theory on the homogenization of second order elliptic equations with random oscillatory coefficients. If time permits, I will continue with stochastic homogenization of some fully nonlinear equations, such as that of Hamilton-Jacobi equations in random environments.