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 they 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 versus iCCA are distinct, but these conditions have overlapping risk factors and pathways of oncogenesis.