The herbivorous sauropod dinosaurs of the Jurassic and Cretaceous periods were the largest terrestrial animals ever, surpassing the largest herbivorous mammals by an order of magnitude in body mass. Several evolutionary lineages among Sauropoda produced giants with body masses in excess of 50 metric tonnes by conservative estimates. With body mass increase driven by the selective advantages of large body size, animal lineages will increase in body size until they reach the limit determined by the interplay of bauplan, biology, and resource availability. There is no evidence, however, that resource availability and global physicochemical parameters were different enough in the Mesozoic to have led to sauropod gigantism. We review the biology of sauropod dinosaurs in detail and posit that sauropod gigantism was made possible by a specific combination of plesiomorphic characters (phylogenetic heritage) and evolutionary innovations at different levels which triggered a remarkable evolutionary cascade. Of these key innovations, the most important probably was the very long neck, the most conspicuous feature of the sauropod bauplan. Compared to other herbivores, the long neck allowed more efficient food uptake than in other large herbivores by covering a much larger feeding envelope and making food accessible that was out of the reach of other herbivores. Sauropods thus must have been able to take up more energy from their environment than other herbivores. The long neck, in turn, could only evolve because of the small head and the extensive pneumatization of the sauropod axial skeleton, lightening the neck. The small head was possible because food was ingested without mastication. Both mastication and a gastric mill would have limited food uptake rate. Scaling relationships between gastrointestinal tract size and basal metabolic rate (BMR) suggest that sauropods compensated for the lack of particle reduction with long retention times, even at high uptake rates. The extensive pneumatization of the axial skeleton resulted from the evolution of an avian-style respiratory system, presumably at the base of Saurischia. An avian-style respiratory system would also have lowered the cost of breathing, reduced specific gravity, and may have been important in removing excess body heat. Another crucial innovation inherited from basal dinosaurs was a high BMR. This is required for fueling the high growth rate necessary for a multi-tonne animal to survive to reproductive maturity. The retention of the plesiomorphic oviparous mode of reproduction appears to have been critical as well, allowing much faster population recovery than in megaherbivore mammals. Sauropods produced numerous but small offspring each season while land mammals show a negative correlation of reproductive output to body size. This permitted lower population densities in sauropods than in megaherbivore mammals but larger individuals. Our work on sauropod dinosaurs thus informs us about evolutionary limits to body size in other groups of herbivorous terrestrial tetrapods. Ectothermic reptiles are strongly limited by their low BMR, remaining small. Mammals are limited by their extensive mastication and their vivipary, while ornithsichian dinosaurs were only limited by their extensive mastication, having greater average body sizes than mammals.