Hepatitis C virus has been identified a quarter of a decade ago as a leading cause of chronic viral hepatitis that can lead to cirrhosis and hepatocellular carcinoma. Only a minority of patients can clear the virus spontaneously during acute infection. Elimination of HCV during acute infection correlates with a rapid induction of innate, especially interferon (IFN) induced genes, and a delayed induction of adaptive immune responses. However, the majority of patients is unable to clear the virus and develops viral persistence in face of an ongoing innate and adaptive immune response. The virus has developed several strategies to escape these immune responses. For example, to escape innate immunity, the HCV NS3/4A protease can efficiently cleave and inactivate two important signalling molecules in the sensory pathways that react to HCV pathogen-associated molecular patterns (PAMPs) to induce IFNs, i.e., the mitochondrial anti-viral signalling protein (MAVS) and the Toll-IL-1 receptor-domain-containing adaptor-inducing IFN-β (TRIF). Despite these escape mechanisms, IFN-stimulated genes (ISGs) are induced in a large proportion of patients with chronic infection. Of note, chronically HCV infected patients with constitutive IFN-stimulated gene (ISG) expression have a poor response to treatment with pegylated IFN-α (PegIFN-α) and ribavirin. The mechanisms that protect HCV from IFN-mediated innate immune reactions are not entirely understood, but might involve blockade of ISG protein translation at the ribosome, localization of viral replication to cell compartments that are not accessible to anti-viral IFN-stimulated effector systems, or direct antagonism of effector systems by viral proteins. Escape from adaptive immune responses can be achieved by emergence of viral escape mutations that avoid recognition by antibodies and T cells. In addition, chronic infection is characterized by the presence of functionally and phenotypically altered NK and T cell responses that are unable to clear the virus but most likely contribute to the ongoing liver disease. In this review, we will summarize current knowledge about the role of innate and adaptive immune responses in determining the outcome of HCV infection.