Abstract:  Transonic flows arise naturally from many important physical phenomena, such as gases in rocket engines and around aircrafts. In this talk, I will focus on transonic shocks in infinite nozzles. The flows are governed by compressible Euler equations. I will talk about the settings and main results. Also, some technical details will be mentioned related to shocks and elliptic estimates. We conclude the stability of transonic flows in the nozzles near constant states.