Haemangiopericytoma (HPC) was described in 1942 by Stout and Murray as a distinctive soft tissue neoplasm, presumably of pericytic origin, exhibiting a characteristic well-developed ‘staghorn’ branching vascular pattern. Over the years, it appeared that this growth pattern was a non-specific one, shared by numerous, unrelated benign and malignant lesions, and that HPC was better considered as a diagnosis of exclusion. Three categories of lesion may now be individualized within the heterogeneous group of HPC-like neoplasms. The first category corresponds to those non-HPC neoplasms that occasionally display HPC-like features (e.g. synovial sarcoma). Lesions belonging to the second category show clear evidence of myoid/pericytic differentiation and correspond to true HPCs. They generally show a benign clinical course, and include glomangiopericytoma/myopericytoma, infantile myofibromatosis (previously called infantile HPC), and a subset of sinonasal HPCs. The third category is the solitary fibrous tumour (SFT) lesional group, which includes fibrous-to-cellular SFTs, and related lesions such as giant cell angiofibromas and lipomatous HPCs. In practice, any HPC-like lesion can be allocated to one of these categories, leaving the ill-defined ‘haemangiopericytoma’ category empty.