Abstract concepts ("freedom") differ from concrete ones ("cat"), as they do not have a bounded, identifiable, and clearly perceivable referent. The way in which abstract concepts are represented has recently become a topic of intense debate, especially because of the spread of the embodied approach to cognition. Within this framework concepts derive their meaning from the same perception, motor, and emotional systems that are involved in online interaction with the world. Most of the evidence in favor of this view, however, has been gathered with regard to concrete concepts. Given the relevance of abstract concepts for higher-order cognition, we argue that being able to explain how they are represented is a crucial challenge that any theory of cognition needs to address. The aim of this article is to offer a critical review of the latest theories on abstract concepts, focusing on embodied ones. Starting with theories that question the distinction between abstract and concrete concepts, we review theories claiming that abstract concepts are grounded in metaphors, in situations and introspection, and in emotion. We then introduce multiple representation theories, according to which abstract concepts evoke both sensorimotor and linguistic information. We argue that the most promising approach is given by multiple representation views that combine an embodied perspective with the recognition of the importance of linguistic and social experience. We conclude by discussing whether or not a single theoretical framework might be able to explain all different varieties of abstract concepts.