Systems approaches to understanding the structure, organisation and functioning of organisms and cells are now becoming commonplace. In this chapter we focus on protein interaction networks and their potential use for inference on the evolutionary processes that have shaped the interactome, the collection of all proteins in a cell together with their physical interactions. We demonstrate that simple mathematical models may capture essential aspects of the processes and use these to develop a Bayesian likelihood-free scheme for inference on three small organisms T. pallidum, H. pylori and P. falciparum.