The rapid diversification and high species richness of flowering plants is regarded as ‘Darwin’s second abominable mystery’. Today the global spatiotemporal pattern of plant diversification remains elusive. Using a newly generated genus-level phylogeny and global distribution data for 14,244 flowering plant genera, we describe the diversification dynamics of angiosperms through space and time. Our analyses show that diversification rates increased throughout the early Cretaceous and then slightly decreased or remained mostly stable until the end of the Cretaceous–Paleogene mass extinction event 66 million years ago. After that, diversification rates increased again towards the present. Younger genera with high diversification rates dominate temperate and dryland regions, whereas old genera with low diversification dominate the tropics. This leads to a negative correlation between spatial patterns of diversification and genus diversity. Our findings suggest that global changes since the Cenozoic shaped the patterns of flowering plant diversity and support an emerging consensus that diversification rates are higher outside the tropics.