Viral polymerases replicate and transcribe the genomes of several viruses of global health concern such as Hepatitis C virus (HCV), human immunodeficiency virus (HIV) and Ebola virus. For this reason they are key targets for therapies to treat viral infections. Although there is little sequence similarity across the different types of viral polymerases, all of them present a right-hand shape and certain structural motifs that are highly conserved. These features allow their functional properties to be compared, with the goal of broadly applying the knowledge acquired from studying specific viral polymerases to other viral polymerases about which less is known. Here we review the structural and functional properties of the HCV RNA-dependent RNA polymerase (NS5B) in order to understand the fundamental processes underlying the replication of viral genomes. We discuss recent insights into the process by which RNA replication occurs in NS5B as well as the role that conformational changes play in this process.