In The Secret of Our Success, Joseph Henrich claims that human beings are unique—different from all other animals—because we engage in cumulative cultural evolution. It is the technological and social products of cumulative cultural evolution, not the intrinsic rationality or ‘smartness’ of individual humans, that enable us to live in a huge range of different habitats, and to dominate most of the creatures who share those habitats with us. We are sympathetic to this general view, the latest expression of the ‘California school’s’ view of cultural evolution, and impressed by the lively and interesting way that Henrich handles evidence from anthropology, economics, and many fields of biology. However, because we think it is time for cultural evolutionists to get down to details, this essay review raises questions about Henrich’s analysis of both the cognitive processes and the selection processes that contribute to cumulative cultural evolution. In the former case, we argue that cultural evolutionists need to make more extensive use of cognitive science, and to consider the evidence that mechanisms of cultural learning are products as well as processes of cultural evolution. In the latter case, we ask whether the California school is really serious about selection, or whether it is offering a merely ‘kinetic’ view of cultural evolution, and, assuming the former, outline four potential models of cultural selection that it would be helpful to distinguish more clearly.