Invasive coronary angiography is the gold standard for the primary diagnosis of coronary artery disease (CAD). At most, only every other examination leads to revascularization therapy. The other coronary angiographies could be replaced by non-invasive examinations. Diagnosing CAD by cardiac MRI and CT can utilize three different strategies: detection of coronary calcifications; imaging of coronary artery stenoses; and detection of restricted myocardial perfusion reserve. Applications are coronary calcification scoring by CT, coronary angiography by MRI or CT, stress cine MRI, and stress perfusion MRI. All these methods are currently used clinically because of their high negative predictive value, i.e., a normal result mostly rules out a hemodynamically significant CAD. For a reasonable implication in clinical practice, however, the pre-test probability must be considered to avoid needless examinations. High pre-test probability invariably demands invasive coronary angiography for planning or performing revascularization therapy. Intermediate pre-test probability, on the contrary, justifies to defer further imaging studies if MRI or CT is normal. Thus, adequate selection of patients for cardiac MRI and CT may reduce the number of invasive coronary angiographies in the future.