Despite decades of research, the roles of climate and humans in driving the dramatic extinctions of large-bodied mammals during the Late Quaternary period remain contentious. Here we use ancient DNA, species distribution models and the human fossil record to elucidate how climate and humans shaped the demographic history of woolly rhinoceros, woolly mammoth, wild horse, reindeer, bison and musk ox. We show that climate has been a major driver of population change over the past 50,000 years. However, each species responds differently to the effects of climatic shifts, habitat redistribution and human encroachment. Although climate change alone can explain the extinction of some species, such as Eurasian musk ox and woolly rhinoceros, a combination of climatic and anthropogenic effects appears to be responsible for the extinction of others, including Eurasian steppe bison and wild horse. We find no genetic signature or any distinctive range dynamics distinguishing extinct from surviving species, emphasizing the challenges associated with predicting future responses of extant mammals to climate and human-mediated habitat change.