This article summarizes my research in biomimetic chemistry on the design and study of functional models for the active sites of metalloproteins such as hemoglobin, myoglobin, and cytochrome c oxidase. Particular emphasis is placed on the results which have shed light on aspects of biological systems hidden from view by the large protein components of the biological molecules. This account was presented in the form of a lecture at the ACS National Meeting, San Francisco, April 1997. The lecture was given in acceptance of the Alfred Bader Award in Bioinorganic or Bioorganic Chemistry.