Despite decades of surveillance and pharmaceutical and non-pharmaceutical interventions, seasonal influenza viruses continue to cause epidemics around the world each year. The key process underlying these recurrent epidemics is the evolution of the viruses to escape the immunity that is induced by prior infection or vaccination. Although we are beginning to understand the processes that underlie the evolutionary dynamics of seasonal influenza viruses, the timing and nature of emergence of new virus strains remain mostly unpredictable. In this Review, we discuss recent advances in understanding the molecular determinants of influenza virus immune escape, sources of evolutionary selection pressure, population dynamics of influenza viruses and prospects for better influenza virus control.