Influenza virus continues to cause yearly seasonal epidemics worldwide and periodically pandemics. Although influenza virus infection and its epidemiology have been extensively studied, a new pandemic is likely. One of the reasons influenza virus causes epidemics is its ability to constantly antigenically transform through genetic diversification. However, host immune defense mechanisms also have the potential to evolve during short or longer periods of evolutionary time. In this mini-review, we describe the evolutionary procedures related with influenza viruses and their hosts, under the prism of a predator-prey relationship.