The process of angiogenesis encompasses the growth and regression of capillary blood vessels. Angiogenesis is finely regulated at the molecular and genetic levels, not unlike other physiologic processes such as coagulation, glucose metabolism, and blood pressure. During the development of the field of angiogenesis research over the past three decades, fundamental concepts have been introduced along the way in an attempt where possible, to unify new data from a variety of different laboratories. I have assembled here the major concepts which underlie the angiogenic process as we currently understand it. Many of these are now taken for granted, but this was not always the case, and I have tried to show how they were developed. My goal is to provide a conceptual framework for those basic scientists or clinicians who may enter this rapidly expanding field. Each concept discussed here is accompanied by a few key references as a guide to the pertinent literature.