Diet composition is among the most important yet least understood dimensions of animal ecology. Inspired by the study of species abundance distributions (SADs), we tested for generalities in the structure of vertebrate diets by characterising them as dietary abundance distributions (DADs). We compiled data on 1167 population‐level diets, representing >500 species from six vertebrate classes, spanning all continents and oceans. DADs near‐universally (92.5%) followed a hollow‐curve shape, with scant support for other plausible rank‐abundance‐distribution shapes. This strong generality is inherently related to, yet incompletely explained by, the SADs of available food taxa. By quantifying dietary generalisation as the half‐saturation point of the cumulative distribution of dietary abundance (sp50, minimum number of foods required to account for 50% of diet), we found that vertebrate populations are surprisingly specialised: in most populations, fewer than three foods accounted for at least half the diet. Variation in sp50 was strongly associated with consumer type, with carnivores being more specialised than herbivores or omnivores. Other methodological (sampling method and effort, taxonomic resolution), biological (body mass, frugivory) and biogeographic (latitude) factors influenced sp50 to varying degrees. Future challenges include identifying the mechanisms underpinning the hollow‐curve DAD, its generality beyond vertebrates, and the biological determinants of dietary generalisation. [ABSTRACT FROM AUTHOR]