Critically ill patients frequently exhibit indirect signs of tissue hypoxia such as metabolic acidosis or elevated blood lactate levels. According to the concept of supply dependence of oxygen uptake (VO2), improvement of tissue oxygenation and secondary reduced mortality rates may be achieved in critically ill patients by an increase in systemic oxygen transport (DO2). However, a critical review of available clinical data and studies suggests that a positive correlation between calculated VO2 and oxygen delivery does not necessarily imply "pathological" oxygen-supply dependence. Possible pitfalls in the interpretation of data are mathematical coupling of data, alterations of oxygen demand, and calorigenic effects of catecholamines. Due to cellular dysfunction in specific tissues, increases in blood lactate concentration in patients with severe sepsis are not proof of tissue hypoxia. Retrospective analyses of data from survivors of critical illnesses form the basis of the therapeutic concept of maximising DO2 to supranormal values. Volume expansion, erythrocytes, catecholamines, and vasoactive agents were used to reach this aim. The results of two studies suggest that beginning the optimisation of DO2 preoperatively may be beneficial in high-risk surgical patients. There is evidence, however, that therapeutic interventions designed to achieve supranormal values of cardiac output, DO2, or VO2 in a heterogeneous population of critically ill patients do not result in reduced morbidity or mortality.