Given a uniform supersonic  incoming flow past a straight wedge, the shock condition gives  two solutions downstream and correspondingly two shocks -- strong and weak shocks. I will talk about the stability of both strong and weak transonic shocks past a 2-D wedge  and how the physical states of the shocks relate to the regularity and asymptotic behavior of the downstream subsonic flows. The talk is based on the joint work with Gui-Qiang Chen and Mikhail Feldman.