In this talk we will start with discussion of shock reflection phenomena. Then we describe recent results on existence and stability of global solutions to regular shock reflection for potential flow for all wedge angles up to the sonic angle, and discuss the techniques. The approach is to reduce the shock reflection problem to a free boundary problem for a nonlinear elliptic equation, with ellipticity degenerate near a part of the boundary (the sonic arc). We will discuss techniques to handle such free boundary problems and degenerate elliptic equations. This is a joint work with Gui-Qiang Chen.