With the latest all-oral interferon- and ribavirin-free regimens based on direct acting antivirals against the hepatitis C virus (HCV), sustained virological response rates of >90% are achieved, which is equivalent to cure. This has become possible for all genotypes and all subgroups of patients, including many of the most difficult-to-treat populations so far. Since a prophylactic HCV vaccine is not yet available, control of HCV infection will for the time being have to rely on the use of effective and safe antiviral treatments as well as their accessibility and affordability. Different approaches may apply to different parts of the world, eradication of HCV representing a major long-term goal. Whether hepatitis C becomes the first chronic viral infection to be eradicated without a prophylactic vaccine remains to be shown. Here, we briefly summarize advances in the molecular virology of hepatitis C, highlight lessons of biological relevance that were learned through the study of HCV, and its translational and clinical implications. We have also listed selected unsolved challenges, emphasizing that HCV is a unique model and that advances in this direction may yield knowledge of broad biological significance, novel technologies and insights into related important human pathogens.