The Circulatory System. The heart, the blood, and the blood vessels make up a system for the transport of gases, nutrients, and chemical wastes. The primary functions of the circulatory system are the following: 1  To transport nutrients and oxygen to the cells. 2  To remove waste and carbon dioxide from the cells.rteries-these carry oxygen rich blood away from the heart, except in the case of the artery to the lungs. 2. Capillaries-these are the sites of gas exchange between the tissues. 3. Veins-these return oxygen poor blood to the heart, except for the vein that carries blood from the lungs.