Grooming is a widespread activity throughout the animal kingdom, but in primates (including humans) social grooming, or allo-grooming (the grooming of others), plays a particularly important role in social bonding which, in turn, has a major impact on an individual's lifetime reproductive fitness. New evidence from comparative brain analyses suggests that primates have social relationships of a qualitatively different kind to those found in other animal species, and I suggest that, in primates, social grooming has acquired a new function of supporting these. I review the evidence for a neuropeptide basis for social bonding, and draw attention to the fact that the neuroendrocrine pathways involved are quite unresolved. Despite recent claims for the central importance of oxytocin, there is equally good, but invariably ignored, evidence for a role for endorphins. I suggest that these two neuropeptide families may play different roles in the processes of social bonding in primates and non-primates, and that more experimental work will be needed to tease them apart.