We use the term regulatory traits to indicate traits that both regulate cultural transmission (e.g., from whom to learn) and are themselves culturally transmitted. In the first part of this contribution we study the dynamics of some of these traits through simple mathematical models. In particular, we consider the cultural evolution of traits that determine the propensity to copy others, the ability to influence others, the number of individuals from whom one may copy, and the number of individuals one tries to influence. We then show how to extend these simple models to address more complex human cultural phenomena, such as in-group biases, the emergence of open or conservative societies, and of cyclical, fashion-like, increases and decreases of popularity of cultural traits. We finally discuss how the ubiquity of regulatory traits in cultural evolution impacts on the analogy between genetic and cultural evolution and therefore on the possibility of using models inspired by evolutionary biology to study human cultural dynamics.