We review recent results related to the approximation of the Burgers equation using the totally asymmetric simple exclusion process. The goal is to show the existence of shocks at a microscopic level. The approach aims at simplicity rather than explicit technical details. First we discuss the graphical representation of the process and coupling, techniques which are used to describe the set of invariant measures for the process. We then obtain law of large numbers and central limit theorems for the shock. Some related cellular automata are reviewed.
AMS Classification numbers: 60K35