Myocardial infarction with non-obstructive coronary arteries (MINOCA), and ischemia with non-obstructive coronary arteries (INOCA) are controversial concepts. A non-obstructive lesion with ≤ 50% stenosis in acute coronary syndromes may have an atherosclerosis process with plaque erosion or fracture and thrombus formation, which are time-dependent and not easily shown by intravascular imaging methods. The largest MINOCA Registry is the Swedish, which included 9,092 patients with MINOCA, supported only by coronary angiography without intravascular imaging, led to unknown dissection, erosion, or fracture, and did not discriminate Takotsubo, myocarditis, or cardiomyopathies. MINOCA must have positive cardiac markers or enzymes, electrocardiographic (ECG) changes, regional wall motion abnormalities (WMA), coronary angiography, and intravascular image to confirm the diagnosis. In INOCA a positive ischemic stress test, coronary angiography, and coronary hyperemic physiologic studies as fractional flow reserve (FFR), and coronary flow reserve (CFR) should be present to confirm the diagnosis.