Organoids are self-organized, three-dimensional structures derived from stem cells that can mimic the structure and physiology of human organs. Patient-specific induced pluripotent stem cells (iPSCs) and 3D organoid model systems allow cells to be analyzed in a controlled environment to simulate the characteristics of a given disease by modeling the underlying pathophysiology. The recent development of 3D cell models has offered the scientific community an exceptionally valuable tool in the study of rare diseases, overcoming the limited availability of biological samples and the limitations of animal models. This review provides an overview of iPSC models and genetic engineering techniques used to develop organoids. In particular, some of the models applied to the study of rare neuronal, muscular and skeletal diseases are described. Furthermore, the limitations and potential of developing new therapeutic approaches are discussed.