The availability of the first molecular clone of the hepatitis C virus (HCV) genome allowed the identification and biochemical characterization of two viral enzymes that are targets for antiviral therapy: the protease NS3-4A and the RNA-dependent RNA polymerase NS5B. With the advent of cell culture systems that can recapitulate either the intracellular steps of the viral replication cycle or the complete cycle, additional drug targets have been identified, most notably the phosphoprotein NS5A, but also host cell factors that promote viral replication, such as cyclophilin A. Here, we review insights into the structures of these proteins and the mechanisms by which they contribute to the HCV replication cycle, and discuss how these insights have facilitated the development of new, directly acting antiviral compounds that have started to enter the clinic.