Aim: The origin of Neotropical hyperdiversity is one of the most intriguing questions in modern biogeography and is best answered through the investigation of large, pantropically distributed genera, allowing the comparison of closely related clades in different regions. We produced a dated phylogeny and reconstructed ancestral ranges of the megadiverse, Andean-centred genus Begonia to discern its dispersal history throughout the Neotropics and correlates of range evolution. Neotropical and Palaeotropical diversification rates were estimated. Location: Neotropics: Central America, South America, West Indies and Mexico. Methods: Plastid DNA sequence data from species representing the full geographical range and majority of sections of Neotropical Begonia were analysed with a secondarily calibrated relaxed molecular clock in order to estimate the age of crown groups and divergence times within Neotropical Begonia. Ancestral areas were reconstructed with a Bayesian approach to dispersal-vicariance analysis, a likelihood framework under a dispersal-extinction-cladogenesis model, and a Bayesian binary method. Diversification rates were estimated under a Bayesian framework. Results: Biogeographical reconstruction indicated two independent trans-Atlantic colonizations of the Neotropics from Africa. Early-diverging lineages of both clades are reconstructed as having diversified in the mid-Miocene, with multiple dispersal events between the Brazilian Atlantic rain forest and the Andes, and single radiations within the West Indies and Central America plus Mexico. Main conclusions: Begonia displays numerous radiations within regions, punctuated by long-distance dispersal. Successful colonization and diversification is predicted by the presence of upland habitat. Recognizing the role of chance dispersal events between available habitats is vital for understanding the formation of current biogeographical patterns.