Contributions of general design theory (GDT) proposed by Yoshikawa for the development of advanced CAD (computer-aided design) and for innovative design from the research results of a group at the University of Tokyo are illustrated. First, the GDT that formalizes design knowledge based on axiomatic set theory is reviewed. Second, this theoretical result is tested against experimental work on design processes. Although in principle the theoretical results agree with the experimental findings, some problems can be pointed out. From these problems a new design process model, called the refinement model, is established, which has better agreement with the experimental findings. This model implies three guiding principles in developing a future CAD system. One is that future CAD requires a mechanism for physics-centered modeling and multiple model management. Second, a mechanism for function modeling is also required, and the FBS (function-behavior-state) modeling is proposed. Third, intention modeling is also proposed for recording decision-making processes in design. These advanced modeling techniques enable creative, innovative designs. As an example, the design of self-maintenance machines is illustrated. This design example utilizes design knowledge intensively on a knowledge-intensive CAD. This is a new way of engineering and can be called knowledge-intensive engineering. The design of self-maintenance machines is, therefore, an example of knowledge-intensive design of knowledge-intensive products, which demonstrates the power of the design methodology derived from the GDT.