The leukodystrophies are rare and serious genetic disorders of the central nervous system that primarily affect children who frequently die early in life or have significantly delayed motor and mental milestones that result in long-term disability. Although with some of these disorders, early intervention with bone marrow or cord blood transplantation has been proven useful, it has not yet been determined that such therapies promote myelin repair of the central nervous system. Research on experimental therapies aimed at myelin repair is aided by the ability to test cell replacement strategies in genetic models in which the mutations and neuropathology match the human disorder. Thus, models exist of Pelizaeus-Merzbacher disease and the lysosomal storage disorder, Krabbe disease, which reflect the clinical and pathological course of the human disorders. Collectively, animals with mutations in myelin genes are called the myelin mutants, and they include rodent models such as the shiverer mouse that have been extensively used to study myelination by exogenous cell transplantation. These studies have encompassed many permutations of the age of the recipient, type of transplanted cell, site of engraftment, and so forth, and they offer hope that the scaling up of myelin produced by transplanted cells will have clinical significance in treating patients. Here we review these models and discuss their relative importance and use in such translational approaches. We discuss how grafts are identified and functional outcomes are measured. Finally, we briefly discuss the cells that have been successfully transplanted, which may be used in future clinical trials.