Coronary artery disease, CAD, is associated with both narrowing of the epicardial coronary arteries and microvascular disease, thereby limiting coronary flow and myocardial perfusion. CAD accounts for almost 2 million deaths within the European Union on an annual basis. In this paper, we review the physiological and pathophysiological processes underlying clinical decision making in coronary disease as well as the models for interpretation of the underlying physiological mechanisms. Presently, clinical decision making is based on non-invasive magnetic resonance imaging, MRI, of myocardial perfusion and invasive coronary hemodynamic measurements of coronary pressure and Doppler flow velocity signals obtained during catheterization. Within the euHeart project, several innovations have been developed and applied to improve diagnosis-based understanding of the underlying biophysical processes. Specifically, MRI perfusion data interpretation has been advanced by the gradientogram, a novel graphical representation of the spatiotemporal myocardial perfusion gradient. For hemodynamic data, functional indices of coronary stenosis severity that do not depend on maximal vasodilation are proposed and the Valsalva maneuver for indicating the extravascular resistance component of the coronary circulation has been introduced. Complementary to these advances, model innovation has been directed to the porous elastic model coupled to a one-dimensional model of the epicardial arteries. The importance of model development is related to the integration of information from different modalities, which in isolation often result in conflicting treatment recommendations.