Hepatitis C virus (HCV) is an unusual RNA virus that has a striking capacity to persist for the remaining life of the host in the majority of infected individuals. In order to persist, HCV must balance viral RNA synthesis and decay in infected cells. In this Review, we focus on interactions between the positive-sense RNA genome of HCV and the host RNA-binding proteins and microRNAs, and describe how these interactions influence the competing processes of viral RNA synthesis and decay to achieve stable, long-term persistence of the viral genome. Furthermore, we discuss how these processes affect hepatitis C pathogenesis and therapeutic strategies against HCV.