In this talk we will start with discussion of shock reflection phenomena, and von Neumann conjectures on transition between regular and Mach reflections. Then we describe the results on existence, uniqueness, stability and regularity of global solutions to shock reflection for potential flow, and discuss the techniques. The approach is to reduce the shock reflection problem to a free boundary problem for a nonlinear elliptic equation in self-similar coordinates, with ellipticity degenerate near a part of the boundary. We will also discuss the open problems in the area.