The field of regenerative medicine is approaching translation to clinical practice, and significant safety concerns and knowledge gaps have become clear as clinical practitioners are considering the potential risks and benefits of cell-based therapy. It is necessary to understand the full spectrum of stem cell actions and preclinical evidence for safety and therapeutic efficacy. The role of animal models for gaining this information has increased substantially. There is an urgent need for novel animal models to expand the range of current studies, most of which have been conducted in rodents. Extant models are providing important information but have limitations for a variety of disease categories and can have different size and physiology relative to humans. These differences can preclude the ability to reproduce the results of animal-based preclinical studies in human trials. Larger animal species, such as rabbits, dogs, pigs, sheep, goats, and non-human primates, are better predictors of responses in humans than are rodents, but in each case it will be necessary to choose the best model for a specific application. There is a wide spectrum of potential stem cell-based products that can be used for regenerative medicine, including embryonic and induced pluripotent stem cells, somatic stem cells, and differentiated cellular progeny. The state of knowledge and availability of these cells from large animals vary among species. In most cases, significant effort is required for establishing and characterizing cell lines, comparing behavior to human analogs, and testing potential applications. Stem cell-based therapies present significant safety challenges, which cannot be addressed by traditional procedures and require the development of new protocols and test systems, for which the rigorous use of larger animal species more closely resembling human behavior will be required. In this article, we discuss the current status and challenges of and several major directions for the future development of large animal models to facilitate advances in stem cell-based regenerative medicine.