Stem cells, as subjects of study for use in treating neurological diseases, are envisioned as a replacement for lost neurons and glia, a means of trophic support, a therapeutic vehicle, and, more recently, a tool for in vitro modeling to understand disease and to screen and personalize treatments. In this review we analyze the requirements of stem cell-based therapy for clinical translation, advances in stem cell research toward clinical application for neurological disorders, and different animal models used for analysis of these potential therapies. We focus on Parkinson's disease (typically defined by the progressive loss of dopaminergic nigral neurons), stroke (neurodegeneration associated with decreased blood perfusion in the brain), and multiple sclerosis (an autoimmune disorder that generates demyelination, axonal damage, astrocytic scarring, and neurodegeneration in the brain and spinal cord). We chose these disorders for their diversity and the number of people affected by them. An additional important consideration was the availability of multiple animal models in which to test stem cell applications for these diseases. We also discuss the relationship between the limited number of systematic stem cell studies performed in animals, in particular nonhuman primates and the delayed progress in advancing stem cell therapies to clinical success.