Fibrodysplasia ossificans progressiva (FOP) is a genetic condition characterized by massive heterotopic ossification. FOP patients have mutations in the Activin A type I receptor (ACVR1), a bone morphogenetic protein (BMP) receptor. FOP is a progressive and debilitating disease characterized by bone formation flares that often occur after trauma. Since it is often difficult or impossible to obtain large amounts of tissue from human donors due to the risks of inciting more heterotopic bone formation, human induced pluripotent stem cells (hiPSCs) provide an attractive source for establishing in vitro disease models and for applications in drug screening. hiPSCs have the ability to self-renew, allowing researchers to obtain large amounts of starting material. hiPSCs also have the potential to differentiate into any cell type in the body. In this review, we discuss how the application of hiPSC technology to studying FOP has changed our perspectives on FOP disease pathogenesis. We also consider ongoing challenges and emerging opportunities for the use of human iPSCs in drug discovery and regenerative medicine.