Poxviruses are double-stranded DNA viruses with several members displaying restricted host ranges. They are genetically stable with low nucleotide mutation rates compared to other viruses, due to the poxviral high-fidelity DNA polymerase. Despite the low accumulation of mutations per replication cycle, poxvirus genomes can recombine with each other to generate genetically rearranged viruses through recombination, a process directly associated with replication and the aforementioned DNA polymerase. Orthopoxvirus replication is intimately tethered to high frequencies of homologous recombination between co-infecting viruses, duplicated sequences of the same virus, and plasmid DNA transfected into poxvirus-infected cells. Unfortunately, the effect of these genomic alterations on the cellular context for all poxviruses across the family Poxviridae remains elusive. However, emerging sequence data on currently circulating and archived poxviruses, such as the genera orthopoxviruses and capripoxviruses, display a wide degree of divergence. This genetic variability cannot be explained by clonality or genetic drift alone, but are probably a result of significant genomic alterations, such as homologous recombination, gene loss and gain, or gene duplications as the major selection forces acting on viral progeny. The objective of this review is to cross-sectionally overview the currently available findings on natural and laboratory observations of recombination in orthopoxviruses, capripoxviruses, and leporipoxviruses, as well as the possible mechanisms involved. Overall, the reviewed available evidence allows us to conclude that the current state of knowledge is limited in terms of the relevance of genetic variations across even a genus of poxviruses as well as fundamental features governing and precipitating intrinsic gene flow and recombination events.