Hepatitis C virus (HCV) has infected over 170 million people worldwide and creates a huge disease burden due to chronic, progressive liver disease. HCV is a single-stranded, positive sense, RNA virus, member of the Flaviviridae family. The high error rate of RNA-dependent RNA polymerase and the pressure exerted by the host immune system, has driven the evolution of HCV into 7 different genotypes and more than 67 subtypes. HCV evolves by means of different mechanisms of genetic variation. On the one hand, its high mutation rates generate the production of a large number of different but closely related viral variants during infection, usually referred to as a quasispecies. The great quasispecies variability of HCV has also therapeutic implications since the continuous generation and selection of resistant or fitter variants within the quasispecies spectrum might allow viruses to escape control by antiviral drugs. On the other hand HCV exploits recombination to ensure its survival. This enormous viral diversity together with some host factors has made it difficult to control viral dispersal. Current treatment options involve pegylated interferon-α and ribavirin as dual therapy or in combination with a direct-acting antiviral drug, depending on the country. Despite all the efforts put into antiviral therapy studies, eradication of the virus or the development of a preventive vaccine has been unsuccessful so far. This review focuses on current available data reported to date on the genetic mechanisms driving the molecular evolution of HCV populations and its relation with the antiviral therapies designed to control HCV infection.