Cognitive research on creativity is both traditional and innovative. It is traditional in the sense that many of the well-recognized processes, structures, and stores from mainstream cognitive psychology have been used to understand creative thinking. It is innovative because there is a need to understand processes which are not recognized unless one is specifically interested in creativity. Some of these are inherently subjective, a fact which is often disregarded by those hoping for a traditionally scientific analysis. Still, much of the interest in the cognitive sciences concerns how new constructs come into being; and anyone interested in that is in fact thinking about creativity. That is creativity. This article reviews several traditional cognitive topics, including knowledge, memory, classification, judgment, and categorization, and describes how each can influence creative thinking. It also presents an original model of creative thinking with problem finding ideation, and judgmental processes as primary components, and knowledge and motivation as secondary (contributing but not controlling) components. Several issues are covered, including the relegation of motivation, the distinction between declarative and procedural knowledge, and the potential for knowledge to both facilitate and inhibit creative ideation.