The strategy of treating critically ill patients by increasing oxygen delivery and consumption to values previously observed among survivors of critical illness (supranormal values) is based on the belief that (1) tissue hypoxia may persist in critically ill patients despite aggressive early resuscitation to traditional endpoints of adequate tissue perfusion and (2) that increasing oxygen delivery can reverse tissue hypoxia. This article addresses the question of whether increasing oxygen delivery improves outcomes in critically ill patients by reviewing the relationship between whole-body oxygen delivery and consumption and by critically examining the randomized controlled trials that have increased oxygen delivery to supranormal values.