The derivation of dopaminergic neurons from induced pluripotent stem cells brings new hope for a patient-specific, stem cell-based replacement therapy to treat Parkinson's disease (PD) and related neurodegenerative diseases; and this novel cell-based approach has already proven effective in animal models. However, there are several aspects of this procedure that have yet to be optimized to the extent required for translation to an optimal cell-based transplantation protocol in humans. These challenges include pinpointing the optimal graft location, appropriately scaling up the graft volume, and minimizing the risk of chronic immune rejection, among others. To advance this procedure to the clinic, it is imperative that a model that accurately and fully recapitulates characteristics most pertinent to a cell-based transplantation to the human brain is used to optimize key technical aspects of the procedure. Nonhuman primates mimic humans in multiple ways including similarities in genomics, neuroanatomy, neurophysiology, immunogenetics, and age-related changes in immune function. These characteristics are critical to the establishment of a relevant model in which to conduct preclinical studies to optimize the efficacy and safety of cell-based therapeutic approaches to the treatment of PD. Here we review previous studies in rodent models, and emphasize additional advantages afforded by nonhuman primate models in general, and the baboon model in particular, for preclinical optimization of cell-based therapeutic approaches to the treatment of PD and other neurodegenerative diseases. We outline current unresolved challenges to the successful application of stem cell therapies in humans and propose that the baboon model in particular affords a number of traits that render it most useful for preclinical studies designed to overcome these challenges.