The influenza A virus causes a highly contagious respiratory disease that significantly impacts our economy and health. Its replication and transcription is catalyzed by the viral RNA polymerase. This enzyme is also crucial for the virus, because it is involved in the adaptation of zoonotic strains. It is thus of major interest for the development of antiviral therapies and is being intensively studied. In this article, we will discuss recent advances that have improved our knowledge of the structure of the RNA polymerase and how mutations in the polymerase help the virus to spread effectively among new hosts.