Whether maximal oxygen uptake (VO2max) during exercise in healthy subjects reflects limitation of the supply of oxygen to muscle mitochondria or an inability to use oxygen beyond some biochemical limit remains debated. This paper summarizes evidence for the hypothesis that VO2max is limited by O2 supply. How the many steps in the pathway for oxygen interact to determine maximum oxygen supply is analyzed, resulting in a mathematical model of predictive value. A major component of this model is the diffusional transport of oxygen out of the muscle microcirculation. The proportionality between VO2max and the capillary to mitochondrion partial pressure gradient (as FIO2 is altered) supports this hypothesis, but does not exclude the existence of convective heterogeneity of blood flow as a factor contributing to the limitation of VO2max. Although there is no direct method for measuring convective heterogeneity, altering hemoglobin P50 permits distinguishing diffusive from convective elements in limiting VO2max, and both the underlying theory and the results are summarized herein. Our conclusion is that VO2max in health appears limited by the supply of oxygen to the mitochondria, which in turn, depends upon the integrated interaction among all of the diffusive and convective steps in the oxygen pathway between the environment and the mitochondria.