Coronary arteries supply blood to the heart muscle. Like all other tissues in the body, the heart muscle needs oxygen-rich blood to function, and oxygen-depleted blood must be carried away.The coronary arteries consist of two main arteries: the right and left coronary arteries.The left coronary artery system branches into the circumflex artery and the left anterior descending artery.oronary arteries supply blood to the heart muscle. Like all other tissues in the body, the heart muscle needs oxygen-rich blood to function, and oxygen-depleted blood must be carried away.