To explain how abstract concepts are grounded in sensory-motor experiences, several theories have been proposed. I will discuss two of these proposals, Conceptual Metaphor Theory and Situated Cognition, and argue why they do not fully explain grounding. A central idea in Conceptual Metaphor Theory is that image schemas ground abstract concepts in concrete experiences. Image schemas might themselves be abstractions, however, and therefore do not solve the grounding problem. Moreover, image schemas are too simple to explain the full richness of abstract concepts. Situated cognition might provide such richness. Research in our laboratory, however, has shown that even for concrete concepts, sensory-motor grounding is task dependent. Therefore, it is questionable whether abstract concepts can be significantly grounded in sensory-motor processing.