Aim: We used frogs of the clade Allocentroleniae (Centrolenidae + Allophrynidae; c. 170 species endemic to Neotropical rain forests) as a model system to address the historical biogeography and diversification of Neotropical rain forest biotas. Location: Neotropical rain forests. Methods: We used an extensive taxon (109 species) and gene (seven nuclear and three mitochondrial genes) sampling to estimate phylogenetic relationships, divergence times, ancestral area distributions, dispersal-vicariance events, and the temporal pattern of diversification rate. Results: The Allocentroleniae started to diversify in the Eocene in South America and by the early Miocene were present in all major Neotropical rain forests except in Central America, which was colonized through 11 late range expansions. The initial uplifts of the Andes during the Oligocene and early Miocene, as well as marine incursions in the lowlands, are coincidental with our estimates of the divergence times of most clades of Allocentroleniae. Clades with broad elevational distributions occupy more biogeographical areas. Most dispersals involve the Andes as a source area but the majority were between the Central and the Northern Andes, suggesting that the Andes did not play a major role as a species pump for the lowlands. The diversification of glassfrogs does not follow a south-to-north pattern of speciation for Andean clades, and the establishment of a transcontinental Amazon drainage system is coincidental in time with the isolation of the Atlantic Forest glassfrogs. Diversification analyses indicated that a model of constantly increasing diversity best fits the data, compatible with the 'evolutionary museum' hypothesis or 'ancient cradle' hypothesis. Main conclusions: Our work illustrates how the different geological and climatic historical events of the Neotropics shaped, at different levels of the phylogeny, the diversity of a species-rich clade, highlighting the importance of studying large evolutionary radiations at a continental scale.