Cultural evolution requires the social transmission of information. For this reason, scholars have emphasized social learning when explaining how and why culture evolves. Yet cultural evolution results from many mechanisms operating in concert. Here, we argue that the emphasis on social learning has distracted scholars from appreciating both the full range of mechanisms contributing to cultural evolution and how interactions among those mechanisms and other factors affect the output of cultural evolution. We examine understudied mechanisms and other factors and call for a more inclusive programme of investigation that probes multiple levels of the organization, spanning the neural, cognitive-behavioural and populational levels. To guide our discussion, we focus on factors involved in three core topics of cultural evolution: the emergence of culture, the emergence of cumulative cultural evolution and the design of cultural traits. Studying mechanisms across levels can add explanatory power while revealing gaps and misconceptions in our knowledge. This article is part of the theme issue ‘Foundations of cultural evolution’.