Heterotopic ossification (HO) is a disorder characterised by the formation of ectopic bone in soft tissue. Acquired HO typically occurs in response to trauma and is relatively common, yet its aetiology remains poorly understood. Genetic forms, by contrast, are very rare, but provide insights into the mechanisms of HO pathobiology. Fibrodysplasia ossificans progressiva (FOP) is the most debilitating form of HO. All patients reported to date carry heterozygous gain-of-function mutations in the gene encoding activin A receptor type I (ACVR1). These mutations cause dysregulated bone morphogenetic protein (BMP) signalling, leading to HO at extraskeletal sites including, but not limited to, muscles, ligaments, tendons and fascia. Ever since the identification of the causative gene, developing a cure for FOP has been a focus of investigation, and studies have decoded the pathophysiology at the molecular and cellular levels, and explored novel management strategies. Based on the established role of BMP signalling throughout HO in FOP, therapeutic modalities that target multiple levels of the signalling cascade have been designed, and some drugs have entered clinical trials, holding out hope of a cure. A potential role of other signalling pathways that could influence the dysregulated BMP signalling and present alternative therapeutic targets remains a matter of debate. Here, we review the recent FOP literature, including pathophysiology, clinical aspects, animal models and current management strategies. We also consider how this research can inform our understanding of other types of HO and highlight some of the remaining knowledge gaps.