This chapter examines how organizations act as self-adapting, complex systems, and how they manage to creatively maintain their existence on the edge of chaos, foster complexity, and renew themselves. The overall shift in academic thought that has given rise to these theories, and this terminology is also examined, with an emphasis on the ways various terms have been used in previous literature. The chapter also reviews the literature on, and develops working definitions of four main characteristic dimensions of organizations: organizational intelligence, organizational stupidity, psychological organizational health, and physical organizational health. Finally, the chapter gives information about research currently being conducted by the authors. This research will attempt to produce a model that represents how organizations are able to exist on the edge of chaos, based on concrete measurements of the four dimensions mentioned above, taken over certain limited time spans.