More than 20 years after the identification of the hepatitis C virus (HCV) as a novel human pathogen, the only approved treatment remains a combination of pegylated interferon-α and ribavirin. This rather non-specific therapy is associated with severe side effects and by far not everyone benefits from treatment. Recently, progress has been made in the development of specifically targeted antiviral therapy for HCV (STAT-C). A major target for such direct acting antivirals (DAAs) is the HCV RNA-dependent RNA polymerase or non-structural protein 5B (NS5B), which is essential for viral replication. This review will examine the current state of development of inhibitors targeting the polymerase and issues such as the emergence of antiviral resistance during treatment, as well as strategies to address this problem.