Induced pluripotent stem cells (iPSCs) have provided new opportunities to explore the cell biology and pathophysiology of human diseases, and the lysosomal storage disorder research community has been quick to adopt this technology. Patient-derived iPSC models have been generated for a number of lysosomal storage disorders, including Gaucher disease, Pompe disease, Fabry disease, metachromatic leukodystrophy, the neuronal ceroid lipofuscinoses, Niemann-Pick types A and C1, and several of the mucopolysaccharidoses. Here, we review the strategies employed for reprogramming and differentiation, as well as insights into disease etiology gleaned from the currently available models. Examples are provided to illustrate how iPSC-derived models can be employed to develop new therapeutic strategies for these disorders. We also discuss how models of these rare diseases could contribute to an enhanced understanding of more common neurodegenerative disorders such as Parkinson's disease, and discuss key challenges and opportunities in this area of research.