Disturbances in bone morphogenetic protein (BMP) signalling contribute to onset and development of a number of rare genetic diseases, including Fibrodysplasia ossificans progressiva (FOP), Pulmonary arterial hypertension (PAH), and Hereditary haemorrhagic telangiectasia (HHT). After decades of animal research to build a solid foundation in understanding the underlying molecular mechanisms, the progressive implementation of iPSC-based patient-derived models will improve drug development by addressing drug efficacy, specificity, and toxicity in a complex humanized environment. We will review the current state of literature on iPSC-derived model systems in this field, with special emphasis on the access to patient source material and the complications that may come with it. Given the essential role of BMPs during embryonic development and stem cell differentiation, gain- or loss-of-function mutations in the BMP signalling pathway may compromise iPSC generation, maintenance, and differentiation procedures. This review highlights the need for careful optimization of the protocols used. Finally, we will discuss recent developments towards complex in vitro culture models aiming to resemble specific tissue microenvironments with multi-faceted cellular inputs, such as cell mechanics and ECM together with organoids, organ-on-chip, and microfluidic technologies.