Hepatitis B, C and D viruses (HBV, HCV, HDV, respectively) specifically infect human hepatocytes and often establish chronic viral infections of the liver, thus escaping antiviral immunity for years. Like other viruses, hepatitis viruses rely on the cellular machinery to meet their energy and metabolite requirements for replication. Although this was initially considered passive parasitism, studies have shown that hepatitis viruses actively rewire cellular metabolism through molecular interactions with specific enzymes such as glucokinase, the first rate-limiting enzyme of glycolysis. As part of research efforts in the field of immunometabolism, it has also been shown that metabolic changes induced by viruses could have a direct impact on the innate antiviral response. Conversely, detection of viral components by innate immunity receptors not only triggers the activation of the antiviral defense but also induces in-depth metabolic reprogramming that is essential to support immunological functions. Altogether, these complex triangular interactions between viral components, innate immunity and hepatocyte metabolism may explain why chronic hepatitis infections progressively lead to liver inflammation and progression to cirrhosis, fibrosis and hepatocellular carcinoma (HCC). In this manuscript, we first present a global overview of known connections between the innate antiviral response and cellular metabolism. We then report known molecular mechanisms by which hepatitis viruses interfere with cellular metabolism in hepatocytes and discuss potential consequences on the innate immune response. Finally, we present evidence that drugs targeting hepatocyte metabolism could be used as an innovative strategy not only to deprive viruses of key metabolites, but also to restore the innate antiviral response that is necessary to clear infection.