The conceptual system contains categorical knowledge about experience that supports the spectrum of cognitive processes. Cognitive science theories assume that categorical knowledge resides in a modular and amodal semantic memory, whereas neuroscience theories assume that categorical knowledge is grounded in the brain's modal systems for perception, action, and affect. Neuroscience has influenced theories of the conceptual system by stressing principles of neural processing in neural networks and by motivating grounded theories of cognition, which propose that simulations of experience represent knowledge. Cognitive science has influenced theories of the conceptual system by documenting conceptual phenomena and symbolic operations that must be grounded in the brain. Significant progress in understanding the conceptual system is most likely to occur if cognitive and neural approaches achieve successful integration.