Abstract Primary liver cancer is the second leading cause of cancer-related death worldwide and therefore a major public health challenge. We review hypotheses of the cell of origin of liver tumorigenesis, and clarify the classes of liver cancer, based on molecular features and how these affect patient prognosis. Primary liver cancer comprises hepatocellular carcinoma (HCC), intrahepatic cholangiocarcinoma (iCCA), and other rare tumors, notably fibrolamellar carcinoma and hepatoblastoma. The molecular and clinical features of HCC vs iCCA are distinct, although they have overlapping risk factors and pathways of oncogenesis. A better understanding of the cell types originating liver cancer can aid in exploring molecular mechanisms of carcinogenesis and therapeutic options. Molecular studies have identified adult hepatocytes as the cell of origin. These cells have been proposed to transform directly into HCC cells (via a sequence of genetic alterations), to de-differentiate into hepatocyte precursor cells (which then become HCC cells that express progenitor cell markers), or to trans-differentiate into biliary-like cells (which give rise to iCCA). Alternatively, progenitor cells also give rise to HCCs and iCCAs with markers of progenitor cells. Advances in genome profiling and next-generation sequencing have led to the classification of HCCs based on molecular features, and assigned them to categories such as proliferation–progenitor, proliferation–transforming growth factor beta, and Wnt–catenin beta 1. iCCAs have been assigned to categories of proliferation and inflammation. Overall, proliferation subclasses are associated with a more aggressive phenotype and poor outcome of patients, although more specific signatures have refined our prognostic abilities. Analyses of genetic alterations have identified those that might be targeted therapeutically, such as fusions in the FGFR2 gene and mutations in genes encoding isocitrate dehydrogenases (in approximately 60% of iCCAs) or amplifications at 11q13 and 6p21 (in approximately 30% of HCCs). Further studies of these alterations are needed before these can be used as biomarkers in clinical decision making.