New treatments for chronic hepatitis C combining direct-acting antivirals (DAAs) with pegylated interferon and ribavirin (PEG-IFN/RBV) have dramatically increased the number of patients whose viral load declines to undetectable levels early in treatment. Most go on to achieve a sustained virologic response, but some patients who maintain undetectable levels of virus throughout treatment later relapse during follow-up. These data suggest that hepatitis C virus (HCV) genomes may persist in form (s) that are refractory to eradication by DAAs and PEG-IFN/RBV. Here we examine the molecular biology of HCV replication and review the clinical virology of relapse for clues as to how the virus might survive months of antiviral therapy to later reappear when treatment is withdrawn.