The negative-sense RNA genome of influenza A virus is composed of eight segments, which encode 12 proteins between them. At the final stage of viral assembly, these genomic virion (v)RNAs are incorporated into the virion as it buds from the apical plasma membrane of the cell. Genome segmentation confers evolutionary advantages on the virus, but also poses a problem during virion assembly as at least one copy of each of the eight segments is required to produce a fully infectious virus particle. Historically, arguments have been presented in favour of a specific packaging mechanism that ensures incorporation of a full genome complement, as well as for an alternative model in which segments are chosen at random but packaged in sufficient numbers to ensure that a reasonable proportion of virions are viable. The question has seen a resurgence of interest in recent years leading to a consensus that the vast majority of virions contain no more than eight segments and that a specific mechanism does indeed function to select one copy of each vRNA. This review summarizes work leading to this conclusion. In addition, we describe recent progress in identifying the specific packaging signals and discuss likely mechanisms by which these RNA elements might operate.