Hepatocellular carcinoma and intrahepatic cholangiocarcinoma are two distinct forms of primary liver carcinoma recognizable at the microscope by their architectural and cytological characteristics, as well as specific immunohistochemical profiles. This straightforward concept however, is increasing imperiled by the recognition of primary liver carcinomas that do not subscribe to a dichotomous paradigm of differentiation, and instead demonstrate biphenotypic differentiation, stem/progenitor cell like features or other variant patterns of differentiation. Appropriate nomenclature, diagnostic criteria, prognostic significance and optimal therapeutic approach for these variant tumors are not completely defined, not leasyt because they are not always identified correctly and when they are, lack of uniform terminology hinders collection of adequate number of cases to facilitate their study. Similar to hepatocellular carcinoma and in contrast with intrahepatic cholangiocarcinoma, primary liver tumors showing biphenotypic differentiation, stem/progenitor cell features or variant differentiation occur mainly, but not always, on a background of chronic liver disease. They are particularly frequent after neo-adjuvant therapy. Whether they represent trans-differentiation of malignant cells, or whether they derive from a stem/progenitor cell that gives rise to divergent differentiation remains yet another area of uncertainty.