Proteins are composed of domains, which are conserved evolutionary units that often also correspond to functional units and can frequently be detected with reasonable reliability using computational methods. Most proteins consist of two or more domains, giving rise to a variety of combinations of domains. Another level of complexity arises because proteins themselves can form complexes with small molecules, nucleic acids and other proteins. The networks of both domain combinations and protein interactions can be conceptualised as graphs, and these graphs can be analysed conveniently by computational methods. In this review we summarise facts and hypotheses about the evolution of domains in multi-domain proteins and protein complexes, and the tools and data resources available to study them.