AbstractAimAlmost half of the extant species of Crocodylia (nine genera, sensu Benton & Clark) belong to the genus Crocodylus, which originated in the Miocene. Today, this genus has a circumtropical distribution, with representatives found in Asia, Oceania, Africa and the Neotropics. However, its geographical origin and the historical events behind its rapid diversification and global radiation are still debated. Here, we inferred the evolution of a set of life traits that aid in dispersal and how they influenced the biogeography of Crocodylus.LocationGlobal.Time periodCretaceous to the present.Major taxa studiedCrocodylidae.MethodsWe estimated biogeographical history on a published phylogeny using probabilistic biogeography models. Next, we identified four life traits likely to promote range expansion and used a trait‐based dispersal model jointly to infer evolution of these traits and their influence on the dispersal of crocodilians. Finally, we used diversification analyses to identify shifts in diversification rates.ResultsAn Asian origin was reconstructed for Crocodylus. Despite the small size of the phylogeny, statistical model comparison reports substantially improved the model fit of trait‐dependent over trait‐independent dispersal models. In individual tests, the four life traits considered (salt tolerance, large size, large clutches and habitat generalism) appear to be correlated statistically with higher dispersal probabilities. However, the traits are likely to be correlated with each other, and we hypothesize that they all reflect the gradual evolution of a range‐expansion phenotype in early Crocodylus that resulted in increased diversification of the clade.Main conclusionsIncreased dispersal in the genus Crocodylus was associated with the gradual evolution of a range‐expansion phenotype. Interestingly, the evolution of the range‐expansion phenotype was also associated with the diversification of the genus in a period of global crocodilian extinction, indicating that range expansion might have served as a potential driver of speciation. This suggests that the concept of “spatial sorting”, normally applied at the population genetic level at the leading edge of an expanding population, might also act on a macroevolutionary scale.