PEComas (tumours showing perivascular epithelioid cell differentiation) are a family of related mesenchymal neoplasms that include angiomyolipoma, lymphangiomyomatosis, clear cell ‘sugar’ tumour of the lung, and a group of rare, morphologically and immunophenotypically similar lesions arising at a variety of visceral and soft tissue sites. These tumours all share a distinctive cell type, the perivascular epithelioid cell or ‘PEC’ (which has no known normal tissue counterpart). PEComas show a marked female predominance and are composed of nests and sheets of usually epithelioid but occasionally spindled cells with clear to granular eosinophilic cytoplasm and a focal association with blood vessel walls. PEComas appear to arise most commonly at visceral (especially gastrointestinal and uterine), retroperitoneal, and abdominopelvic sites, with a subset occurring in somatic soft tissue and skin. Nearly all PEComas show immunoreactivity for both melanocytic (HMB‐45 and/or melan‐A) and smooth muscle (actin and/or desmin) markers. A subset of PEComas behave in a malignant fashion. This review examines the members of the PEComa family, with an emphasis on lesions arising outside of the kidney, lung and liver, and discusses preliminary evidence for pathological features that might predict malignant behaviour.