The geological record of South American mammals is spatially biased because productive fossil sites are concentrated at high latitudes. As a result, the history of mammalian diversification in Amazonia and other tropical biomes is largely unknown. Here we report diversification analyses based on a time-calibrated molecular phylogeny of opossums (Didelphidae), a species-rich clade of mostly tropical marsupials descended from a Late Oligocene common ancestor. Optimizations of habitat and geography on this phylogeny suggest that (1) basal didelphid lineages inhabited South American moist forests; (2) didelphids did not diversify in dry-forest habitats until the Late Miocene; and (3) most didelphid lineages did not enter North America until the Pliocene. We also summarize evidence for an Early- to Middle-Miocene mass extinction event, for which alternative causal explanations are discussed. To the best of our knowledge, this study provides the first published molecular-phylogenetic evidence for mass extinction in any animal clade, and it is the first time that evidence for such an event (in any plant or animal taxon) has been tested for statistical significance. Potentially falsifying observations that could help discriminate between the proposed alternative explanations for didelphid mass extinction may be obtainable from diversification analyses of other sympatric mammalian groups.