Hypometric scaling of aerobic metabolism [larger organisms have lower mass-specific metabolic rates (MR/g)] is nearly universal for interspecific comparisons among animals, yet we lack an agreed upon explanation for this pattern. If physiological constraints on the function of larger animals occur and limit MR/g, these should be observable as direct constraints on animals of extant species and/or as evolved responses to compensate for the proposed constraint. There is evidence for direct constraints and compensatory responses to O2 supply constraint in skin-breathing animals, but not in vertebrates with gas-exchange organs. The duration of food retention in the gut is longer for larger birds and mammals, consistent with a direct constraint on nutrient uptake across the gut wall, but there is little evidence for evolving compensatory responses to gut transport constraints in larger animals. Larger placental mammals (but not marsupials or birds) show evidence of greater challenges with heat dissipation, but there is little evidence for compensatory adaptations to enhance heat loss in larger endotherms, suggesting that metabolic rate (MR) more generally balances heat loss for thermoregulation in endotherms. Size-dependent patterns in many molecular, physiological, and morphological properties are consistent with size-dependent natural selection, such as stronger selection for neurolocomotor performance and growth rate in smaller animals and stronger selection for safety and longevity in larger animals. Hypometric scaling of MR very likely arises from different mechanisms in different taxa and conditions, consistent with the diversity of scaling slopes for MR.