The latter part of the last glaciation, 50,000-12,000 years ago (kya), was characterized by a rapidly changing climate, cold conditions and corresponding vegetation and faunal turnover. It also coincided with the extinction of the Neanderthals and the expansion of modern human populations. Established views of modern human superiority over Neanderthals as the cause of their extinction are under attack as recent work shows that Neanderthals were capable of behaviour that is regarded as modern. As we discuss here, the exact nature of biological and cultural interactions between Neanderthals and other human groups between 50 kya and 30 kya is currently hotly contested. The extinction of the Neanderthals, and other modern human lineages, now appears to have been a drawn-out, climate-related affair.