Homogenization theory in nonlinear partial differential equations

In this paper, we are going to consider recent works in Homogenization Theory in Nonlinear Partial Differential Equations, which concerns the derivation of a macroscopic homogenized (or effective) equation for the system with oscillating microscopic structures. Mainly we focus on topics related with the homogenization for high oscillation, nonvariational problems, lower dimensional oscillations or equations of nondivergence type.