AbstractAimThe Neotropics currently host outstanding levels of species richness, with one‐third of the global tetrapod species. The underlying causes of these extraordinary levels of biodiversity are a topic debated in evolutionary ecology, but the main processes at work remain elusive.LocationNeotropics.Time periodCenozoic and Mesozoic.Major taxa studiedTetrapods.MethodsUsing global phylogenies for amphibians, birds, lepidosaurs and mammals, biogeographical and time‐variable (trait‐dependent and trait‐independent) diversification models, we examined changes in speciation and extinction rates through time in the Neotropics in relationship to other areas of the world, and estimated the time of Neotropical colonizations.ResultsWe found that from the origin of lepidosaurs and mammals until the Pliocene (the Miocene for birds), diversification rates within the Neotropics were lower than rates in other regions (i.e., turnover was high). Afterwards, extinction decreased relative to speciation, and Neotropical diversification outpaced diversification in other regions. Dispersal out of the Neotropics also increased after the Pliocene (the Miocene for birds), exceeding into‐the‐Neotropics migrations. For amphibians, diversification rates in the Neotropics have been higher than in other areas through time, and dispersal out of the Neotropics decreased in the Cenozoic.Main conclusionsThe common view that the Neotropics are an ancient source of world species diversity, with high in situ speciation, dispersal to other areas and low extinction, might be true only for amphibians. For mammals, birds and lepidosaurs, the Neotropics acted as a diversity sink from their origin until the Miocene–Pliocene (i.e., diversification rates were lower and turnover higher than in other areas). Only afterwards did the region turn into a diversity source. Our study highlights that models accounting for rates of diversification that vary through time could improve our capacity to assess evolutionary dynamics over long time‐scales.