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Cultural traits originate through creative or innovative processes, which might be crucial to understanding how culture evolves and accumulates. However, because of its complexity and apparent subjectivity, creativity has remained largely unexplored as the dynamic underpinning of cultural evolution. Here, we explore the approach to innovation commonly taken in theoretical studies of cultural evolution and discuss its limitations. Drawing insights from cognitive science, psychology, archeology, and even animal behavior, it is possible to generate a formal description of creativity and to incorporate a dynamic theory of creativity into models of cultural evolution. We discuss the implications of such models for our understanding of the archaeological record and the history of hominid culture.