Blood is pumped into the cardiac muscle through arteries called the coronary arteries. Over time, the accumulation of cholesterol, coagulation factors, and cells on the walls of these arteries causes the walls to thicken and lose their elasticity, resulting in the development of atherosclerosis. When the blood supply of the heart is diminished by atherosclerosis, it can be restored by bypass surgery, in which atherosclerosis-free vein and/ or artery grafts taken from another area of the body are used to replace the atherosclerotic vessels. These biological grafts used in surgery differ in biochemical composition and long-term patency. Although the great saphenous vein (GSV) has been the most popular graft material in revascularization for years, it has recently been superseded by the internal mammarian artery (IMA), which has a lower incidence of recurrence of atherosclerosis. The aim of the present review is briefly to address the structure of the cardiovascular system and blood vessels, and then, in the light recent data, to present the biochemical compositions and individual advantages of the graft materials used to restore an impaired blood supply to the heart.