Influenza is probably one of the oldest viruses in the world, and it is still evolving. The 1918-1919 influenza pandemic killed 21 million people around the world. It is the sixth most important cause of death in the United States. The persistence of influenza depends on its ability to evolve in its host (antigenic shift and genetic drift); so that new strains and subtypes of the virus appear and old ones reappear. To understand the workings of the influenza A virus, dynamic models are required at both the cellular and population levels. Furthermore, to develop effective treatment and control strategies, one must link these micro and macro models so that the evolution of the virus within its hosts is related to its dynamics in communities and worldwide. I will give a survey talk about dynamic epidemiolgical models of the spread of influenza A, emphasizing important directions for future research.