Climate change may be a major threat to global biodiversity, potentially leading to the extinction of many species. But how many? There have been various attempts to answer this question, sometimes yielding strikingly different estimates. Here we review these estimates, assess their discrepancies and methodology, and explore how we might arrive at better estimates. Large-scale studies have estimated extinctions of ~1 % of sampled species by up to ~70 %, even using the same approach (species distribution models; SDM). However, worst-case estimates often approximate species losses in the neighborhood of 20 %–30 %, and many of the differences shrink when similar assumptions are used. We conduct a new review of recent SDM studies that show ~17% of species loss due to climate change in the worst-case scenarios. However, this review shows that many SDM studies are biased by excluding the most vulnerable species (those known from few locations), which can lead to an underestimation of global species loss. In contrast, our analyses of recent responses to climate change show that the basic assumption of SDM studies, that species' climatic niches do not change over time, can often be violated. (JJohn J. Wiens, Joseph Zelinka)