Anti-angiogenic therapies are being pursued as means of starving tumors of their energy supply. While numerous studies show that such therapies render tumors hypoxic, just as many studies have, surprisingly, shown improved tumor oxygenation. These contradicting findings challenge both the original rationale for anti-angiogenic therapy and our understanding of the physiology of tissue oxygenation. The flow-diffusion equation, which describes the relation between blood flow and the extraction of freely diffusible molecules in tissue, was recently extended to take the heterogeneity of capillary transit times (CTH) into account. CTH is likely to be high in the chaotic microvasculature of a tumor, increasing the effective shunting of blood through its capillary bed. We review the properties of the extended flow-diffusion equation in tumor tissue. Elevated CTH reduces the extraction of oxygen, glucose, and cytotoxic molecules. The extent to which their net extraction is improved by anti-angiogenic therapy in turn, depends on the extent to which CTH is normalized by the treatment. The extraction of oxygen and glucose are affected to different extents by elevated CTH, and the degree of aerobic glycolysis - known as the Warburg effect - is thus predicted to represent an adaptation to the CTH of the local microvasculature.