A cardiopulmonary bypass system utilizing membrane-based reciprocating positive displacement blood pumps (“pod pumps”). In one aspect, the pod pumps are constructed to provide reduced shear forces on the blood being pumped. In another aspect blood flow through the pod pumps can he controlled by a controller using information from pressure sensors in the control chamber of the pod pumps. In another aspect, the pod pumps are included on a disposable unit that can be received and held by a receptacle means on a base unit, the base unit also providing pressurized control fluid to the pod pumps on the disposable unit through the receptacle means.