A variety of mechanisms for socially facilitated learning allow animals to acquire information from the behaviour of others, and through their own modified behaviour such information can subsequently be transmitted between individuals within and across generations. Variation in such socially acquired and transmitted behaviours is unlikely to be under direct genetic control since individuals who are closely related genetically can have and pass on very different behaviours; this is also true for cultural traditions that such behaviours may have generated. Behavioural information transfer of this nature thus represents another form of inheritance that operates in many nonhuman species, including primates, in tandem with the more basic genetic system. Most behavioural traditions usually precede genetic adaptations but exert persistent directional selection for genetic variations congruent with the new patterns of behaviour since such traditions lead to the transmission of the same selective regime. Selection for the ability to learn a particular behaviour pattern more efficiently and rapidly may also lead to it becoming dependent on fewer learning trials or none at all – ultimately culminating in a partial or complete incorporation of the trait into the basic genetic inheritance system. This paper reviews principles of culture and its biological foundations, and examines the rôles that behavioural inheritance and socially transmitted cultural traditions play in the structure and dynamics of primate societies, with particular reference to data from long-term field studies on Japanese macaques and from bonnet macaques, a species endemic to peninsular India. Three principal consequences are considered: the appearance of individual behavioural traits leading to the establishment of social traditions, the rôle of stable behavioural traditions in facilitating cultural selection, and the influence of particular behavioural and life-history traits on gene-culture coevolution in nonhuman primates.