Genetic recombination is used as a tool for modifying the composition of poxvirus genomes in both discovery and applied research. This review documents the history behind the development of these tools as well as what has been learned about the processes that catalyze virus recombination and the links between it and DNA replication and repair. The study of poxvirus recombination extends back to the 1930s with the discovery that one virus can reactivate another by a process later shown to generate recombinants. In the years that followed it was shown that recombinants can be produced in virus-by-virus crosses within a genus (e.g., variola-by-rabbitpox) and efforts were made to produce recombination-based genetic maps with modest success. The marker rescue mapping method proved more useful and led to methods for making genetically engineered viruses. Many further insights into the mechanism of recombination have been provided by transfection studies which have shown that this is a high-frequency process associated with hybrid DNA formation and inextricably linked to replication. The links reflect the fact that poxvirus DNA polymerases, specifically the vaccinia virus E9 enzyme, can catalyze strand transfer in in vivo and in vitro reactions dependent on the 3′-to-5′ proofreading exonuclease and enhanced by the I3 replicative single-strand DNA binding protein. These reactions have shaped the composition of virus genomes and are modulated by constraints imposed on virus–virus interactions by viral replication in cytoplasmic factories. As recombination reactions are used for replication fork assembly and repair in many biological systems, further study of these reactions may provide new insights into still poorly understood features of poxvirus DNA replication.