A great deal of research has focused on the question of whether or not concepts are embodied as a rule. Supporters of embodiment have pointed to studies that implicate affective and sensorimotor systems in cognitive tasks, while critics of embodiment have offered nonembodied explanations of these results and pointed to studies that implicate amodal systems. Abstract concepts have tended to be viewed as an important test case in this polemical debate. This essay argues that we need to move beyond a pretheoretical notion of abstraction. Against the background of current research and theory, abstract concepts do not pose a single, unified problem for embodied cognition but, instead, three distinct problems: the problem of generalization, the problem of flexibility, and the problem of disembodiment. Identifying these problems provides a conceptual framework for critically evaluating, and perhaps improving upon, recent theoretical proposals.