The error-prone replication and life cycle of influenza virus generate a diverse set of genetic variants. Transmission between hosts strictly limits both the number of virus particles and the genetic diversity of virus variants that reach a new host and establish an infection. This sharp reduction in the virus population at transmission--the transmission bottleneck--is significant to the evolution of influenza virus and to its epidemic and pandemic potential. This review describes transmission bottlenecks and their effect on the diversity and evolution of influenza virus. It also reviews the methods for calculating and predicting bottleneck sizes and highlights the host and viral determinants of influenza transmissibility.