Gigantism-very large body size-is an ecologically important trait associated with competitive superiority. Although it has been studied in particular cases, the general conditions for the evolution and maintenance of gigantism remain obscure. I compiled sizes and dates for the largest species in 3 terrestrial and 7 marine trophic and habitat categories of animals from throughout the Phanerozoic. The largest species (global giants) in all categories are of post-Paleozoic age. Gigantism at this level appeared tens to hundreds of millions of years after mass extinctions and long after the origins of clades in which it evolved. Marine gigantism correlates with high planktic or seafloor productivity, but on land the correspondence between productivity and gigantism is weak at best. All global giants are aerobically active animals, not gentle giants with low metabolic demands. Oxygen concentration in the atmosphere correlates with gigantism in the Paleozoic but not thereafter, likely because of the elaboration of efficient gas-exchange systems in clades containing giants. Although temperature and habitat size are important in the evolution of very large size in some cases, the most important (and rare) enabling circumstance is a highly developed ecological infrastructure in which essential resources are abundant and effectively recycled and reused, permitting activity levels to increase and setting the stage for gigantic animals to evolve. Gigantism as a hallmark of competitive superiority appears to have lost its luster on land after the Mesozoic in favor of alternative means of achieving dominance, especially including social organization and coordinated food-gathering.