Global linguistic diversity reflects the gradual gain and loss of languages over millennia, yet half of the world’s ~6-7000 languages are threatened with extinction by the end of this century. Attempts to identify factors that promote or reduce linguistic diversity have focused largely on the correlates of current language richness (languages per unit area) and threat status. However, much less work has examined how linguistic diversity is shaped by evolutionary history and the processes of lineage diversification and extinction that underlie it. Here, we use Bayesian phylogenetic inference techniques to generate a supertree of extant human languages (n=6635) that integrates prior knowledge and uncertainty about linguistic diversification around the globe. Our posterior treeset, which represents more than 10 million years of language change, reveals net diversification rates are higher in regions of moderate population density and landscape traversability, for languages spoken over a larger area and further from cities, and for cultures that are reliant on agriculture and maintain political links beyond the local community. By combining our global tree with data on language threat status we also show that evolutionary distinctness (how distantly related a language is to its closest relatives) is positively related to endangerment, and generate a ranking and map of the world’s most evolutionarily distinct, globally endangered (EDGE) languages. Our findings provide insight into the forces shaping linguistic diversity, indicate more of the evolutionary history of languages is at risk than expected under a random threat distribution, reinforce the need to act now to document and protect this diversity, and pave the way for further refinement of the global tree of human languages.