Transonic flows arise from various physical phenomena. In general, Euler equations are appropriate models for gas dynamics involving shocks. In this talk, I will focus on the wedge problem. When a supersonic flow past a wedge, there will be a shock created attaching to the tip of the wedge, given some subsonic condition in the far field. I will talk about the existence and uniqueness of this type of flows for 2-D steady Euler equations. The Euler system will be reduced to an elliptic equation in subsonic region and some delicate elliptic estimates are needed to solve the problem.