The Price equation is currently considered one of the fundamental equations —or even the fundamental equation— of evolution. In this article, we explore the role of this equation within cultural evolutionary theory. More specifically, we use it to account for the explanatory power and the theoretical structure of a certain generalised version of dual-inheritance theory. First, we argue that, in spite of not having a definite empirical content, the Price equation offers a suitable formalisation of the processes of cultural evolution, (...) and provides a powerful heuristic device for discovering the actual causes of cultural change and accumulation. Second, we argue that, as a consequence of this, a certain version of the Price equation is the fundamental law of cultural evolutionary theory. In order to support this claim, we sketch the ideal structure of dual-inheritance theory and we stress the unificatory role that the Price equation plays in it. (shrink)