Asia’s rich species diversity has been linked to its Cenozoic geodiversity, including active mountain building and dramatic climatic changes. However, prior studies on the diversification and assembly of Asian faunas have been derived mainly from analyses at taxonomic or geographic scales too limited to offer a comprehensive view of this complex region’s biotic evolution. Here, using the class Mammalia, we built historical biogeographic models drawn on phylogenies of 1,543 species occurring across Asia to investigate how and when the mammal diversity in Asian regions and mountain hotspots was assembled. We explore the roles of in situ speciation, colonization, and vicariance and geoclimatic events to explain the buildup of Asia’s regional mammal diversity through time. We found that southern Asia has served as the main cradle of Asia’s mammal diversity. Present-day species richness in other regions is mainly derived from colonization, but by the Miocene, in situ speciation increased in importance. The high biodiversity present in the mountain hotspots (Himalayas and Hengduan) that flank the Qinghai–Tibetan plateau is a product of high colonization instead of in situ speciation, making them important centers of lineage accumulation. Overall, Neogene was marked by great diversification and migrations across Asia and surrounding continents but Paleogene environments already hosted rich mammal assemblages. Our study revealed that synchronous diversification bursts and biotic turnovers are temporally associated with tectonic events (mountain building, continental collisions) and drastic reorganization of climate (aridification of Asian interior, intensification of Asian monsoons, sea retreat) that took place throughout the Cenozoic in Asia.