Creativity results from neural processes that include binding of representations, generation of new concepts and rules, and the application of analogies. The Semantic Pointer Architecture accommodates the full range of multimodal representations needed for creativity in the domains of scientific discovery, technological invention, artistic imagination, and social innovation. New semantic pointers can be generated by convolution-based bindings in ways that produce new and useful images, concepts, rules, and analogies. Procedural creativity is the generation of new methods expressed as rules. The pragmatic focus of creative problem solving and the evaluation of the goal relevance of new products can be carried out by emotions. Competition among semantic pointers explains how the realization that one might have done something creative enters consciousness.