Burials of the Late Palaeolithic (14 000–11 600 cal years before present, henceforth BP) are a rare phenomenon in Europe. Several sites possess burials of single and double individuals. As with the preceding Magdalenian, the burial of more than two individuals in the same grave cutting seems to be unusual, but does occur occasionally. The deposition of isolated and disarticulated human remains with or without cut marks seems additionally to belong to the Magdalenian context. In the final Palaeolithic phase (13 000–11 600 cal years BP) there is evidence for cemetery-like clusters of burials, which contrast to the Magdalenian evidence, instead showing some similarities with the succeeding Mesolithic. The earliest Mesolithic burials 11 600–10 500 cal BP) are a very rare phenomenon, covering a short time span between the beginning of the Preboreal and the beginning of the Boreal phase of the early Holocene. Here the evidence includes single inhumations, cemetery-like structures and a number of isolated human remains. Caves and rock shelters were the most common places for inhumations in both the final Palaeolithic and the early Mesolithic. Although the number of sites with a chronological continuity from the LUP to the Early Mesolithic burial is low, several aspects indicate a general continuity in burial patterns over this period. Apart from this continuity, the Mesolithic burials in general seem to represent a new level of diversity in burial practices. This article is part of the theme issue ‘Evolutionary thanatology: impacts of the dead on the living in humans and other animals’.