Put most simply, heterotopic ossification (HO) is the abnormal formation of bone at extraskeletal sites. HO can be classified into two main subtypes, genetic and acquired. Acquired HO is a common complication of major connective tissue injury, traumatic central nervous system injury, and surgical interventions, where it can cause significant pain and postoperative disability. A particularly devastating form of HO is manifested in the rare genetic disorder, fibrodysplasia ossificans progressiva (FOP), in which progressive heterotopic bone formation occurs throughout life, resulting in painful and disabling cumulative immobility. While the central role of stem/progenitor cell populations in HO is firmly established, the identity of the offending cell type(s) remains to be conclusively determined, and little is known of the mechanisms that direct these progenitor cells to initiate cartilage and bone formation. In this review, we summarize current knowledge of the cells responsible for acquired HO and FOP, highlighting the strengths and weaknesses of animal models used to interrogate the cellular origins of HO.