Summary: This is an expository paper whose goal is to provide a detailed survey without the full technicalities of the methods used recently in the authors’ paper [J. Am. Math. Soc. 18, No. 1, 61–120 (2005; Zbl 1058.35163) and Commun. Pure Appl. Math. 57, No. 2, 141–218 (2004; Zbl 1073.35162)] to prove the existence of curved multi-D viscous shocks, to rigorously justify the small viscosity limit, and to prove long time stability of multidimensional planar viscous shocks.