Pigs play an important role in influenza A virus (IAV) epidemiology because they support replication of human, avian, and swine origin viruses and act as an IAV reservoir for pigs and other species, including humans. Moreover, novel IAVs with human pandemic potential may be generated in pigs. To minimize the threat of IAVs to human and swine health, it is crucial to understand host defense mechanisms that restrict viral replication and pathology in pigs. In this article, we review IAV strains circulating in the North American swine population, as well as porcine innate and acquired immune responses to IAV, including recent advances achieved through immunological tools developed specifically for swine. Furthermore, we highlight unique aspects of the porcine pulmonary immune system, which warrant consideration when developing vaccines and therapeutics to limit IAV in swine or when using pigs to model human IAV infections.