Parallel molecular evolution is the independent evolution of the same genotype or phenotype from distinct ancestors. The simple genomes and rapid evolution of many viruses mean they are useful model systems for studying parallel evolution by natural selection. Parallel adaptation occurs in the context of several viral behaviours, including cross-species transmission, drug resistance, and host immune escape, and its existence suggests that at least some aspects of virus evolution and emergence are repeatable and predictable. We introduce examples of virus parallel evolution and summarise key concepts. We outline the difficulties in detecting parallel adaptation using virus genomes, with a particular focus on phylogenetic and structural approaches, and we discuss future approaches that may improve our understanding of the phenomenon.