Influenza A viruses (IAVs) are the causative agents of one of the most important viral respiratory diseases in pigs and humans. Human and swine IAV are prone to interspecies transmission, leading to regular incursions from human to pig and vice versa. This bidirectional transmission of IAV has heavily influenced the evolutionary history of IAV in both species. Transmission of distinct human seasonal lineages to pigs, followed by sustained within-host transmission and rapid adaptation and evolution, represent a considerable challenge for pig health and production. Consequently, although only subtypes of H1N1, H1N2, and H3N2 are endemic in swine around the world, extensive diversity can be found in the hemagglutinin (HA) and neuraminidase (NA) genes, as well as the remaining six genes. We review the complicated global epidemiology of IAV in swine and the inextricably entangled implications for public health and influenza pandemic planning.