For the past two centuries, non‐human primates have been reported to inspect, protect, retrieve, carry or drag the dead bodies of their conspecifics and, for nearly the same amount of time, sparse scientific attention has been paid to such behaviours. Given that there exists a considerable gap in the fossil and archaeological record concerning how early hominins might have interacted with their dead, extant primates may provide valuable insight into how and in which contexts thanatological behaviours would have occurred. First, we outline a comprehensive history of comparative thanatology in non‐human primates, from the earliest accounts to the present, uncovering the interpretations of previous researchers and their contributions to the field of primate thanatology. Many of the typical behavioural patterns towards the dead seen in the past are consistent with those observed today. Second, we review recent evidence of thanatological responses and organise it into distinct terminologies: direct interactions (physical contact with the corpse) and secondary interactions (guarding the corpse, vigils and visitations). Third, we provide a critical evaluation regarding the form and function of the behavioural and emotional aspects of these responses towards infants and adults, also comparing them with non‐conspecifics. We suggest that thanatological interactions: promote a faster re‐categorisation from living to dead, decrease costly vigilant/caregiving behaviours, are crucial to the management of grieving responses, update position in the group's hierarchy, and accelerate the formation of new social bonds. Fourth, we propose an integrated model of Life‐Death Awareness, whereupon neural circuitry dedicated towards detecting life, i.e. the agency system (animate agency, intentional agency, mentalistic agency) works with a corresponding system that interacts with it on a decision‐making level (animate/inanimate distinction, living/dead discrimination, death awareness). Theoretically, both systems are governed by specific cognitive mechanisms (perceptual categories, associative concepts and high‐order reasoning, respectively). Fifth, we present an evolutionary timeline from rudimentary thanatological responses likely occurring in earlier non‐human primates during the Eocene to the more elaborate mortuary practices attributed to genus Homo throughout the Pleistocene. Finally, we discuss the importance of detailed reports on primate thanatology and propose several empirical avenues to shed further light on this topic. This review expands and builds upon previous attempts to evaluate the body of knowledge on this subject, providing an integrative perspective and bringing together different fields of research to detail the evolutionary, sensory/cognitive, developmental and historical/archaeological aspects of primate thanatology. Considering all these findings and given their cognitive abilities, we argue that non‐human primates are capable of an implicit awareness of death.