An extensive program of research in the past 2 decades has focused on the role of modal sensory, motor, and affective brain systems in storing and retrieving concept knowledge. This focus has led in some circles to an underestimation of the need for more abstract, supramodal conceptual representations in semantic cognition. Evidence for supramodal processing comes from neuroimaging work documenting a large, well-defined cortical network that responds to meaningful stimuli regardless of modal content. The nodes in this network correspond to high-level “convergence zones” that receive broadly crossmodal input and presumably process crossmodal conjunctions. It is proposed that highly conjunctive representations are needed for several critical functions, including capturing conceptual similarity structure, enabling thematic associative relationships independent of conceptual similarity, and providing efficient “chunking” of concept representations for a range of higher order tasks that require concepts to be configured as situations. These hypothesized functions account for a wide range of neuroimaging results showing modulation of the supramodal convergence zone network by associative strength, lexicality, familiarity, imageability, frequency, and semantic compositionality. The evidence supports a hierarchical model of knowledge representation in which modal systems provide a mechanism for concept acquisition and serve to ground individual concepts in external reality, whereas broadly conjunctive, supramodal representations play an equally important role in concept association and situation knowledge.