The concept of oxygen transport, defined as the relation between oxygen consumption (VO2) and delivery (DO2), is of fundamental importance in critically ill patients. The past 200 years have witnessed a stepwise progressive improvement in the understanding of pathophysiological disturbances in the balance of DO2 and VO2 in critically ill patients including those after cardiopulmonary bypass surgery. Intermittent spectacular technological achievements have accelerated the rate of progress. Therapeutic advances have been particularly impressive during the recent decades. Examination of the relation between DO2 and VO2 provides a useful framework around which the care of the critically ill may be developed. Until now, only a few groups have used this framework to examine children after cardiopulmonary bypass. The key topics that will be covered in this review article are the evolution of the concept from its early development to its present, increasingly sophisticated, role in the management of critically ill patients, with a focus on children after cardiopulmonary bypass surgery.