Climate change will have far-reaching impacts on biodiversity, including increasing extinction rates. Current approaches to quantifying such impacts focus on measuring exposure to climatic change and largely ignore the biological differences between species that may significantly increase or reduce their vulnerability. To address this, we present a framework for assessing three dimensions of climate change vulnerability, namely sensitivity, exposure and adaptive capacity; this draws on species' biological traits and their modeled exposure to projected climatic changes. In the largest such assessment to date, we applied this approach to each of the world's birds, amphibians and corals (16,857 species). The resulting assessments identify the species with greatest relative vulnerability to climate change and the geographic areas in which they are concentrated, including the Amazon basin for amphibians and birds, and the central Indo-west Pacific (Coral Triangle) for corals. We found that high concentration areas for species with traits conferring highest sensitivity and lowest adaptive capacity differ from those of highly exposed species, and we identify areas where exposure-based assessments alone may over or under-estimate climate change impacts. We found that 608-851 bird (6-9%), 670-933 amphibian (11-15%), and 47-73 coral species (6-9%) are both highly climate change vulnerable and already threatened with extinction on the IUCN Red List. The remaining highly climate change vulnerable species represent new priorities for conservation. Fewer species are highly climate change vulnerable under lower IPCC SRES emissions scenarios, indicating that reducing greenhouse emissions will reduce climate change driven extinctions. Our study answers the growing call for a more biologically and ecologically inclusive approach to assessing climate change vulnerability. By facilitating independent assessment of the three dimensions of climate change vulnerability, our approach can be used to devise species and area-specific conservation interventions and indices. The priorities we identify will strengthen global strategies to mitigate climate change impacts.