Abstract: The concept of creativity is a central one in folk psychological explanation and has long been prominent in philosophical debates about the nature of art, genius, and the imagination. The scientific investigation of creativity in humans is also well established, and there has been increasing interest in the question of whether the concept can be rigorously applied to non-human animals. In this paper, I argue that such applications face serious challenges of both a conceptual and methodological character, reflecting deep controversies within both philosophy and psychology concerning how to define and apply the concept of creativity. After providing a brief review of some of the leading theories of creativity (Section 2) and discussing some of the strongest putative cases of creative intelligence in non-human animals (Section 3), I examine some of the more worrisome difficulties faced by attempts to use these theories to answer the question of whether animals are truly creative (Section 4). I conclude by examining how we might overcome them, and suggest that one approach worth taking seriously is to adopt what I term a Strong Rejectionist view of creativity, eschewing use of the term entirely in the scientific study of comparative cognition.