Dramatic advances have been made in the last two decades in the diagnosis and treatment of coronary artery disease. The development of open heart surgical techniques for bypassing occluded arteries made quantitative diagnostic techniques more important. Computer enhanced angiographic methods, together with measurements using tomography, ultrasound and magnetic resonance imaging have greatly improved the precision of the diagnosis. A more complete understanding of coronary mechanics and control has enabled physicians to better interpret the significance of geometric information and to supplement this information with functional assessment of stenosed arteries. Finally, traditional bypass surgery is now supplemented with closed-chest techniques such as balloon angioplasty. Biomedical engineers have been involved in all of these developments. This paper will review these developments and attempt to identify remaining questions.