The cacti are one of the most celebrated radiations of succulent plants. There has been much speculation about their age, but progress in dating cactus origins has been hindered by the lack of fossil data for cacti or their close relatives. Using a hybrid phylogenomic approach, we estimated that the cactus lineage diverged from its closest relatives ≈35 million years ago (Ma). However, major diversification events in cacti were more recent, with most species-rich clades originating in the late Miocene, ≈10-5 Ma. Diversification rates of several cactus lineages rival other estimates of extremely rapid speciation in plants. Major cactus radiations were contemporaneous with those of South African ice plants and North American agaves, revealing a simultaneous diversification of several of the world's major succulent plant lineages across multiple continents. This short geological time period also harbored the majority of origins of C(4) photosynthesis and the global rise of C(4) grasslands. A global expansion of arid environments during this time could have provided new ecological opportunity for both succulent and C(4) plant syndromes. Alternatively, recent work has identified a substantial decline in atmospheric CO(2) ≈15-8 Ma, which would have strongly favored C(4) evolution and expansion of C(4)-dominated grasslands. Lowered atmospheric CO(2) would also substantially exacerbate plant water stress in marginally arid environments, providing preadapted succulent plants with a sharp advantage in a broader set of ecological conditions and promoting their rapid diversification across the landscape.