The antigenic drift theory states that influenza evolves via the gradual accumulation of mutations, decreasing a host´s immune protection against previous strains. Influenza vaccines are designed accordingly, under the premise of antigenic drift. However, a paradox exists at the centre of influenza research. If influenza evolved primarily through mutation in multiple epitopes, multiple influenza strains should co-circulate. Such a multitude of strains would render influenza vaccines quickly inefficacious. Instead, a single or limited number of strains dominate circulation each influenza season. Unless additional constraints are placed on the evolution of influenza, antigenic drift does not adequately explain these observations. Here, we explore the constraints placed on antigenic drift and a competing theory of influenza evolution - antigenic thrift. In contrast to antigenic drift, antigenic thrift states that immune selection targets epitopes of limited variability, which constrain the variability of the virus. We explain the implications of antigenic drift and antigenic thrift and explore their current and potential uses in the context of influenza vaccine design.