Approximately 25% of mammals are currently threatened with extinction, a risk that is amplified under climate change. Species persistence under climate change is determined by the combined effects of climatic factors on multiple demographic rates (survival, development and reproduction), and hence, population dynamics. Thus, to quantify which species and regions on Earth are most vulnerable to climate-driven extinction, a global understanding of how different demographic rates respond to climate is urgently needed. Here, we perform a systematic review of literature on demographic responses to climate, focusing on terrestrial mammals, for which extensive demographic data are available. To assess the full spectrum of responses, we synthesize information from studies that quantitatively link climate to multiple demographic rates. We find only 106 such studies, corresponding to 87 mammal species. These 87 species constitute <1% of all terrestrial mammals. Our synthesis reveals a strong mismatch between the locations of demographic studies and the regions and taxa currently recognized as most vulnerable to climate change. Surprisingly, for most mammals and regions sensitive to climate change, holistic demographic responses to climate remain unknown. At the same time, we reveal that filling this knowledge gap is critical as the effects of climate change will operate via complex demographic mechanisms: a vast majority of mammal populations display projected increases in some demographic rates but declines in others, often depending on the specific environmental context, complicating simple projections of population fates. Assessments of population viability under climate change are in critical need to gather data that account for multiple demographic responses, and coordinated actions to assess demography holistically should be prioritized for mammals and other taxa.