“Predictions of species-level extinction risk from climate change are mostly based on species distribution models (SDMs). Reviewing the literature, we summarise why the translation of SDM results to extinction risk is conceptually and methodologically challenged and why critical SDM assumptions are unlikely to be met under climate change. Published SDMderived extinction estimates are based on a positive relationship between range size decline and extinction risk, which empirically is not well understood. Importantly, the classification criteria used by the IUCN Red List of Threatened Species were not meant for this purpose and are often misused. Future predictive studies would profit considerably from a better understanding of the extinction risk-range decline relationship, particularly regarding the persistence and non-random distribution of the few last individuals in dwindling populations. Nevertheless, in the face of the ongoing climate and biodiversity crises, there is a high demand for predictions of future extinction risks. Despite prevailing challenges, we agree that SDMs currently provide the most accessible method to assess climate-related extinction risk across multiple species. We summarise current good practice in how SDMs can serve to classify species into IUCN extinction risk categories and predict whether a species is likely to become threatened under future climate. However, the uncertainties associated with translating predicted range declines into quantitative extinction risk need to be adequately communicated and extinction predictions should only be attempted with carefully conducted SDMs that openly communicate the limitations and uncertainty.” in Cambridge Prisms