In this paper, we explore how experimental studies of cultural transmission in adult humans can address general questions regarding the ‘who, what, when and how’ of human cultural transmission, and consequently inform a theory of human cultural evolution. Three methods are discussed. The transmission chain method, in which information is passed along linear chains of participants, has been used to identify content biases in cultural transmission. These concern the kind of information that is transmitted. Several such candidate content biases have now emerged from the experimental literature. The replacement method, in which participants in groups are gradually replaced or moved across groups, has been used to study phenomena such as cumulative cultural evolution, cultural group selection and cultural innovation. The closed-group method, in which participants learn in groups with no replacement, has been used to explore issues such as who people choose to learn from and when they learn culturally as opposed to individually. A number of the studies reviewed here have received relatively little attention within their own disciplines, but we suggest that these, and future experimental studies of cultural transmission that build on them, can play an important role in a broader science of cultural evolution.