Climate change may be an important threat to global biodiversity, potentially leading to the extinction of numerous 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 disagreements and methodology, and explore how we might reach better estimates. Large-scale studies have estimated the extinction of ~1% of sampled species up to ~70%, even when using the same approach (species distribution models; SDMs). Nevertheless, worst-case estimates often converge near 20%-30% species loss, and many differences shrink when using similar assumptions. We perform a new review of recent SDM studies, which show ~17% loss of species to climate change under worst-case scenarios. However, this review shows that many SDM studies are biased by excluding the most vulnerable species (those known from few localities), which may lead to underestimating global species loss. Conversely, our analyses of recent climate change responses show that a fundamental assumption of SDM studies, that species' climatic niches do not change over time, may be frequently violated. For example, we find mean rates of positive thermal niche change across species of ~0.02°C/year. Yet, these rates may still be slower than projected climate change by ~3-4 fold. Finally, we explore how global extinction levels can be estimated by combining group-specific estimates of species loss with recent group-specific projections of global species richness (including cryptic insect species). These preliminary estimates tentatively forecast climate-related extinction of 14%-32% of macroscopic species in the next ~50 years, potentially including 3-6 million (or more) animal and plant species, even under intermediate climate change scenarios.