Regional species diversity is explained ultimately by speciation, extinction and dispersal. Here, we estimate dispersal and speciation rates of Neotropical butterflies to propose an explanation for the distribution and diversity of extant species. We focused on the tribe Brassolini (owl butterflies and allies), a Neotropical group that comprises 17 genera and 108 species, most of them endemic to rainforest biomes. We inferred a robust species tree using the multispecies coalescent framework and a dataset including molecular and morphological characters. This formed the basis for three changes in Brassolini classification: (1) Naropina syn. nov. is subsumed within Brassolina; (2) Aponarope syn. nov. is subsumed within Narope; and (3) Selenophanes orgetorix comb. nov. is reassigned from Catoblepia to Selenophanes. By applying biogeographical stochastic mapping, we found contrasting species diversification and dispersal dynamics across rainforest biomes, which might be explained, in part, by the geological and environmental history of each bioregion. Our results revealed a mosaic of biome-specific evolutionary histories within the Neotropics, where butterfly species have diversified rapidly (cradles: Mesoamerica), have accumulated gradually (museums: Atlantic Forest) or have diversified and accumulated alternately (Amazonia). Our study contributes evidence from a major butterfly lineage that the Neotropics are a museum and a cradle of species diversity.