Here I discuss two broad versions of human cultural evolution which currently exist in the literature and which emphasise different underlying dynamics. One, which originates in population-genetic-style modelling, emphasises how cultural selection causes some cultural variants to be favoured and gradually increase in frequency over others. The other, which draws more from cognitive science, holds that cultural change is driven by the biased transformation of cultural variants by individuals in non-random and consistent directions. Despite claims that cultural evolution is characterised by one or the other of these dynamics, these are neither mutually exclusive nor a dichotomy. Different domains of human culture are likely to be more or less characterised by cultural selection and biased transformation. Identifying cultural dynamics in real-world cultural data is challenging given that they can generate the same population-level patterns, such as directional change or cross-cultural stability, and the same cognitive and emotional mechanisms may underlie both cultural selection and biased transformation. Nevertheless, fine-grained historical analysis and lab experiments, combined with formal models to generate quantitative predictions, offer the best way of distinguishing them.