Clinical cardiology diagnosis relies on the assessment of a set of specified parameters. Computer modeling is a powerful tool that can provide a realistic interpretation of the variations of these parameters through computational quantification. Here we present an overview of different aspects of diagnosis that are based on evaluation of either systolic or diastolic cardiac abnormalities. Emphasis is on the quantitative hemodynamic assessment and modeling. For myocardial ischemia and stunning, multi-scale modeling from single fiber to the global ventricular level is demonstrated. The classic force-velocity-length relations are found to be applicable even for modern quantitative cardiac assessment. The reduced systolic shortening and delayed diastolic relaxation associated with stunning and ischemia can be reproduced even at the single muscle fiber level. In addition, ejection fraction (EF) which has been viewed as an important index in assessing the state of the heart, is found to be inadequate for the diagnosis and assessment of heart failure (HF) in differentiation of HF patients with reduced EF (HFrEF) or with preserved EF (HFpEF). Parameters that relate to structural changes whether at fiber or the global levels are found to be most appropriate to quantify the cardiac function, hence for its quantitative diagnosis. Parameters that govern heart-arterial system interaction when the LV is single-loaded with pressure-overloaded LV hypertrophy or double-loaded as in LVH with aortic valve stenosis are also quantified. It is shown that a computational modeling approach can be invaluable in delineating parameters that are critical for quantitative cardiology diagnosis.