The introduction of direct-acting antivirals (DAAs) has revolutionized hepatitis C treatment. Short courses of treatment with these drugs are highly beneficial to patients, eliminating hepatitis C virus (HCV) without adverse effects. However, this outstanding success is tempered by the continuing difficulty of eradicating the virus worldwide. Thus, access to an effective vaccine against HCV is strongly needed to reduce the burden of the disease and contribute to the elimination of viral hepatitis. The recent failure of a T-cell vaccine based on the use of viral vectors expressing the HCV non-structural protein sequences to prevent chronic hepatitis C in drug users has pointed out that the induction of neutralizing antibodies (NAbs) will be essential in future vaccine candidates. To induce NAbs, vaccines must contain the main target of this type of antibody, the HCV envelope glycoproteins (E1 and E2). In this review, we summarize the structural regions in E1 and E2 proteins that are targeted by NAbs and how these proteins are presented in the vaccine candidates currently under development.