Worldwide epidemics of influenza are caused by viruses that normally infect other species, particularly waterfowl, and that contain haemagglutinin membrane glycoproteins (HAs) to which the human population has no immunity. Anti‐HA immunoglobulins neutralize influenza virus infectivity. In this review we outline structural differences that distinguish the HAs of the 16 antigenic subtypes (H1–16) found in viruses from avian species. We also describe structural changes in HA required for the effective transfer to humans of viruses containing three of them, H1, H2 and H3, in the 1918 (Spanish), the 1957 (Asian) and the 1968 (Hong Kong) pandemics, respectively. In addition, we consider changes that may be required before the current avian H5 viruses could pass from human to human.