Fibrodysplasia ossificans progressiva (FOP) is a debilitating genetic disorder characterized by recurrent episodes of heterotopic ossification (HO) formation in muscles, tendons, and ligaments. FOP is caused by a missense mutation in the gene (activin A receptor type I), an important signaling receptor involved in endochondral ossification. The mutation induces increased downstream canonical SMAD-signaling and drives tissue-resident progenitor cells with osteogenic potential to participate in endochondral HO formation. In this article, we review aberrant ACVR1 signaling and the cells that give rise to HO in FOP. FOP mouse models and lineage tracing analyses have been used to provide strong evidence for tissue-resident mesenchymal cells as cellular contributors to HO. We assess how the underlying mutation in FOP disrupts muscle-specific dynamics during homeostasis and repair, with a focus on muscle-resident mesenchymal cells known as fibro-adipogenic progenitors (FAPs). Accumulating research points to FAPs as a prominent HO progenitor population, with FAPs not only aberrantly differentiating into chondro-osteogenic lineages but creating a permissive environment for bone formation at the expense of muscle regeneration. We will further discuss the emerging role of FAPs in muscle regeneration and therapeutic targeting of these cells to reduce HO formation in FOP.