The natural history of infection by the hepatitis B virus (HBV) depends on many factors, including the age and immunological status of the patient, and can range from acute transient infection to subclinical chronic hepatitis. Persistent infection often leads to the development of primary hepatocellular carcinoma. We consider a cellular model of HBV infection based on the hypothesis that the liver contains two populations of cells with contrasting responses to the virus. Our findings show that the model can be used to account for the wide variety of clinical manifestations of infection and can explain the observed age dependence of the main different outcomes of the disease.