Mountain ranges harbour exceptionally high biodiversity, which is now under threat from rapid environmental change. However, despite decades of effort, the limited availability of data and analytical tools has prevented a robust and truly global characterization of elevational biodiversity gradients and their evolutionary origins(1,2). This has hampered a general understanding of the processes involved in the assembly and maintenance of montane communities(2-4). Here we show that a worldwide midelevation peak in bird richness is driven by wide-ranging species and disappears when we use a subsampling procedure that ensures even species representation in space and facilitates evolutionary interpretation. Instead, richness corrected for range size declines linearly with increasing elevation. We find that the more depauperate assemblages at higher elevations are characterized by higher rates of diversification across all mountain regions, rejecting the idea that lower recent diversification rates are the general cause of less diverse biota. Across all elevations, assemblages on mountains with high rates of past temperature change exhibit more rapid diversification, highlighting the importance of climatic fluctuations in driving the evolutionary dynamics of mountain biodiversity. While different geomorphological and climatic attributes of mountain regions have been pivotal in determining the remarkable richness gradients observed today, our results underscore the role of ongoing and often very recent diversification processes in maintaining the unique and highly adapted biodiversity of higher elevations.