Abstract Although large diversifications of species occur unevenly across space and evolutionary lineages, the relative importance of their driving mechanisms, such as climate, ecological opportunity and key innovations, remains poorly understood. Here, we explore the remarkable diversification of rhacophorid frogs, which represent six percent of global amphibian diversity, utilize four distinct reproductive modes, and span a climatically variable area across mainland Asia, associated continental islands, and Africa. Using a complete species-level phylogeny, we find near-constant diversification rates but a highly uneven distribution of species richness. Montane regions on islands and some mainland regions have higher phylogenetic diversity and unique assemblages of taxa; we identify these as cool-wet refugia. Starting from a centre of origin, rhacophorids reached these distant refugia by adapting to new climatic conditions (‘niche evolution’-dominant), especially following the origin of key innovations such as terrestrial reproduction (in the Late Eocene) or by dispersal during periods of favourable climate (‘niche conservatism’-dominant).