The climates of Asia are affected significantly by the extent and height of the Himalayan mountains and the Tibetan plateau. Uplift of this region began about 50 Myr ago, and further significant increases in altitude of the Tibetan plateau are thought to have occurred about 10-8 Myr ago, or more recently. However, the climatic consequences of this uplift remain unclear. Here we use records of aeolian sediments from China and marine sediments from the Indian and North Pacific oceans to identify three stages of evolution of Asian climates: first, enhanced aridity in the Asian interior and onset of the Indian and east Asian monsoons, about 9-8 Myr ago; next, continued intensification of the east Asian summer and winter monsoons, together with increased dust transport to the North Pacific Ocean, about 3.6-2.6 Myr ago; and last, increased variability and possible weakening of the Indian and east Asian summer monsoons and continued strengthening of the east Asian winter monsoon since about 2.6 Myr ago. The results of a numerical climate-model experiment, using idealized stepwise increases of mountain-plateau elevation, support the argument that the stages in evolution of Asian monsoons are linked to phases of Himalaya-Tibetan plateau uplift and to Northern Hemisphere glaciation.