Abstract concepts can potentially be represented using metaphorical mappings to concrete domains. This view predicts that when linguistic metaphors are processed, they will invoke sensory-motor simulations. Here, I examine evidence from neuroimaging and lesion studies that addresses whether metaphors in language are embodied in this manner. Given the controversy in this area, I first outline some criteria by which the quality of neuroimaging and lesion studies might be evaluated. I then review studies of metaphors in various sensory-motor domains, such as action, motion, texture, taste, and time, and examine their strengths and weaknesses. Studies of idioms are evaluated next. I also address some neuroimaging studies that can speak to the question of metaphoric conceptual organization without explicit use of linguistic metaphors. I conclude that the weight of the evidence suggests that metaphors are indeed grounded in sensory-motor systems. The case of idioms is less clear, and I suggest that they might be grounded in a qualitatively different manner than metaphors at higher levels of the action hierarchy. While metaphors are unlikely to explain all aspects of abstract concept representation, for some specific abstract concepts, there is also nonlinguistic neural evidence for metaphoric conceptual organization.