Archaeologists have drawn on evolutionary theory for more than three decades resulting in a diversity of approaches that lay claim to being a type of Darwinian archaeology. These are briefly reviewed, and some suggested to be of limited value to the discipline. The paper argues that a valid evolutionary approach requires an explicitly cognitive perspective, and suggests that there will be considerable benefit from an integration between cognitive archaeology and evolutionary psychology. The result would be a non-functionalist Darwinian archaeology with potential to throw new light on cultural developments during the Palaeolithic and more recent times. To illustrate this, the paper discusses the cultural transmission of religious ideas.