Effective innate and adaptive immune responses are essential for the control of hepatitis C virus (HCV) infection. Indeed, elimination of HCV during acute infection correlates with an early induction of innate and a delayed induction of adaptive immune responses. However, in the majority of acutely HCV-infected individuals, these responses are insufficient to clear the virus and persistence develops. In recent years, different mechanisms responsible for the failure of innate and adaptive immune responses have been identified. These include the proteolytic cleavage of molecules playing key roles in the induction of the interferon response, manipulation of interferon-induced effector proteins, interference with CD8+ T-cell function or immune escape in T- and B-cell epitopes. In this review, we discuss the possible roles of innate and adaptive immune responses in HCV clearance and the different evasion strategies used by the virus to escape these immune responses.