Hepatitis C virus (HCV) infections constitute a major public health problem and are the main cause of chronic hepatitis and liver disease worldwide. The existing drugs, while effective, are expensive and associated with undesirable secondary effects. There is, hence, an urgent need to develop novel therapeutics, as well as an effective vaccine to prevent HCV infection. Understanding the interplay between HCV and the host cells will certainly contribute to better comprehend disease progression and may unravel possible new cellular targets for the development of novel antiviral therapeutics. Here, we review and discuss the interplay between HCV and the host cell innate immunity. We focus on the different cellular pathways that respond to, and counteract, HCV infection and highlight the evasion strategies developed by the virus to escape this intracellular response.