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Our growing understanding of the plant tree of life provides a novel opportunity to uncover the major drivers of angiosperm diversity. Using a time-calibrated phylogeny, we characterized hot and cold spots of lineage diversification across the angiosperm tree of life by modeling evolutionary diversification using stepwise AIC (MEDUSA). We also tested the whole-genome duplication (WGD) radiation lag-time model, which postulates that increases in diversification tend to lag behind established WGD events. Diversification rates have been incredibly heterogeneous throughout the evolutionary history of angiosperms and reveal a pattern of ‘nested radiations’ – increases in net diversification nested within other radiations. This pattern in turn generates a negative relationship between clade age and diversity across both families and orders. We suggest that stochastically changing diversification rates across the phylogeny explain these patterns. Finally, we demonstrate significant statistical support for the WGD radiation lag-time model. Across angiosperms, nested shifts in diversification led to an overall increasing rate of net diversification and declining relative extinction rates through time. These diversification shifts are only rarely perfectly associated with WGD events, but commonly follow them after a lag period.