Frogs (Anura) are one of the most diverse groups of vertebrates and comprise nearly 90% of living amphibian species. Their worldwide distribution and diverse biology make them well-suited for assessing fundamental questions in evolution, ecology, and conservation. However, despite their scientific importance, the evolutionary history and tempo of frog diversification remain poorly understood. By using a molecular dataset of unprecedented size, including 88-kb characters from 95 nuclear genes of 156 frog species, in conjunction with 20 fossil-based calibrations, our analyses result in the most strongly supported phylogeny of all major frog lineages and provide a timescale of frog evolution that suggests much younger divergence times than suggested by earlier studies. Unexpectedly, our divergence-time analyses show that three species-rich clades (Hyloidea, Microhylidae, and Natatanura), which together comprise ∼88% of extant anuran species, simultaneously underwent rapid diversification at the Cretaceous-Paleogene (K-Pg) boundary (KPB). Moreover, anuran families and subfamilies containing arboreal species originated near or after the KPB. These results suggest that the K-Pg mass extinction may have triggered explosive radiations of frogs by creating new ecological opportunities. This phylogeny also reveals relationships such as Microhylidae being sister to all other ranoid frogs and African continental lineages of Natatanura forming a clade that is sister to a clade of Eurasian, Indian, Melanesian, and Malagasy lineages. Biogeographical analyses suggest that the ancestral area of modern frogs was Africa, and their current distribution is largely associated with the breakup of Pangaea and subsequent Gondwanan fragmentation. amphibia | Anura | nuclear genes | phylogeny | divergence time