The comparative and evolutionary analysis of social learning and all manner of cultural processes has become a flourishing field. Applying the ‘comparative method’ to such phenomena allows us to exploit the good fortunate we have in being able to study them in satisfying detail in our living primate relatives, using the results to reconstruct the cultural cognition of the ancestral forms we share with these species. Here I offer an overview of principal discoveries in recent years, organized through a developing scheme that targets three main dimensions of culture: the patterning of culturally transmitted traditions in time and space; the underlying social learning processes; and the particular behavioral and psychological contents of cultures. I focus on a comparison between humans, particularly children, and our closest primate relative the chimpanzee, for which we now have much the richest database of relevant observational and experimental findings. Commonalities across these sister-species can be identified in each of the three dimensions listed above and in several subcategories within them, but the comparisons also highlight the major contrasts in the nature of culture that have evolved between ourselves and closest primate relatives.