Given the fundamental role that concepts play in theories of cognition, philosophers and cognitive scientists have a common interest in concepts. Nonetheless, there is a great deal of controversy regarding what kinds of things concepts are, how they are structured, and how they are acquired. This chapter offers a detailed high-level overview and critical evaluation of the main theories of concepts and their motivations. Taking into account the various challenges that each theory faces, the chapter also presents a novel approach to concepts that is organized around two ideas. The first is a pluralistic view of differing types of conceptual structure. The second is a model that treats concepts as atomic representations that are linked to various types of conceptual structures.