Explosive radiations—substantial increases in net species diversification—have been considered one of the most intriguing diversification patterns across the Tree of Life,but the subsequent change,movement,and extinction of the constituent lineages make radiations hard to discern or understand as geological time passes.We used the megadiverse angiosperm genus Solanum L.(Solanaceae),with ca.1200 currently accepted species distributed worldwide in a wide array of habitats,to explore these patterns on a global scale.We synthesized phylogenetic and distributional data for this ongoing radiation to show how dispersal events and past climatic changes have interacted to shape diversification.We find that,despite the vast diversity of Solanum lineages in the Neotropics,lineages in the Old World are diversifying more rapidly.This recent increase in diversification coincides with a long-distance dispersal event from the Neotropics to regions where major climatic changes were taking place.Two separate groups of Solanum have migrated and established in Australia,but only the arid-adapted lineages underwent significant increases in diversification rate,as they were able to adapt to the continent's long-term climatic trend towards seasonally dry and arid biomes(a pattern observed in the diversification of other arid-adapted groups).Our findings provide a clear example of how successful colonization of new areas and niches can—but does not always—drive explosive diversifications.