What happens when plague builds up in blood vessels?

Plaque buildup is the pathophysiology of a disease called Atherosclerosis. These plaque buildups are essentially massive accumulations onto of clots. They are made up of cellular debris, blood cells, platelets, cholesterol, and fatty deposit buildups. The main issue with these buildups is that they continually add stuff on top of it, so they will get progressively bigger, until there is sufficient occlusion of the blood vessel and adequate perfusion of the cells proximal to it has been compromised. These are called Thrombi or stationary clots and they are responsible for MIs (Myocardial Infarctions, or heart attacks), Occlusive CVA's (Cerbrovascular accidents, or strokes) TIA (Transient Ischemic Attacks, or mini strokes), DVT's (Deep Venous Thrombi) etc... These can reach the point where tissues can infarct or die.

Another issue is that these Thrombi can break off forming a traveling clot known as a embolism, which can lodge anywhere including the pulmonary vasculature, which causes pulmonary embolisms.