A carrier system for gases and nutrients became mandatory when primitive animals grew larger and developed different organs. The first circulatory systems are peristaltic tubes pushing slowly the haemolymph into an open vascular tree without capillaries (worms). Arthropods developed contractile bulges on the abdominal aorta assisted by accessory hearts for wings or legs and by abdominal respiratory motions. Two-chamber heart (atrium and ventricle) appeared among mollusks. Vertebrates have a multi-chamber heart and a closed circulation with capillaries. Their heart has two chambers in fishes, three chambers (two atria and one ventricle) in amphibians and reptiles, and four chambers in birds and mammals. The ventricle of reptiles is partially divided in two cavities by an interventricular septum, leaving only a communication of variable size leading to a variable shunt. Blood pressure increases progressively from 15 mmHg (worms) to 170/70 mmHg (birds) according to the increase in metabolic rate. When systemic pressure exceeds 50 mmHg, a lower pressure system appears for the circulation through gills or lungs in order to improve gas exchange. A four-chamber heart allows a complete separation of systemic and pulmonary circuits. This review describes the circulatory pumping systems used in the different classes of animals, their advantages and failures, and the way they have been modified with evolution.