As a group, influenza-A viruses (IAV) infect a wide range of animal hosts, however, they are constrained to infecting selected host species by species-specific interactions between the host and virus, that are required for efficient replication of the viral RNA genome. When IAV cross the species barrier, they acquire mutations in the viral genome to enable interactions with the new host factors, or to compensate for their loss. The viral polymerase genes polymerase basic 1, polymerase basic 2, and polymerase-acidic are important sites of host adaptation. In this review, we discuss why the viral polymerase is so vital to the process of host adaptation, look at some of the known viral mutations, and host factors involved in adaptation, particularly of avian IAV to mammalian hosts.