Influenza infection is initiated by virus attachment to sialic acid-containing cell-surface receptors. The spectrum of sialylglycoconjugates varies substantially between viral host species as well as target tissues and cell types of the same species, leading to variations in the receptor-binding specificity of viruses circulating in these hosts. Therefore, receptor specificity plays an important role in the viral cell and tissue tropism, interspecies transmission and adaptation to a new host, and a poor fit of avian viruses to receptors in humans limits the emergence of new pandemic strains. Adaptation of an avian virus to a mammalian host also involves enhanced activity of the viral polymerase in mammalian cells which, in part, is the result of improved binding of the polymerase to the nuclear import machinery of the cell. These findings suggest that host range and virulence are the result of optimised molecular interactions between viral proteins and cellular factors. Future transmission studies with animals may reveal to what extent haemagglutinin receptor-binding mutations and polymerase-activity-enhancing mutations together enable influenza A viruses to cross species barriers.