While global patterns of human genetic diversity are increasingly well characterized, the diversity of human languages remains less systematically described. Here, we outline the Grambank database. With over 400,000 data points and 2400 languages, Grambank is the largest comparative grammatical database available. The comprehensiveness of Grambank allows us to quantify the relative effects of genealogical inheritance and geographic proximity on the structural diversity of the world's languages, evaluate constraints on linguistic diversity, and identify the world's most unusual languages. An analysis of the consequences of language loss reveals that the reduction in diversity will be strikingly uneven across the major linguistic regions of the world. Without sustained efforts to document and revitalize endangered languages, our linguistic window into human history, cognition, and culture will be seriously fragmented.