In this article we discuss different techniques to solve numerically wave propagation phenomena in unbounded domains. We present in a unified and simple way the two ways to restrict the computation to a finite domain: absorbing (or artificial) boundary conditions (ABC) and perfectly matched layers (PML). The intent is to give the possibility to the reader to grasp easily similarities and differences between these two truncation techniques. It should also allow the reader to adapt a truncation technique to the peculiarities of his physical modeling.