Zika and dengue viruses belong to the Flavivirus genus, a close group of antigenically related viruses that cause significant arthropod‐transmitted diseases throughout the globe. Although infection by a given flavivirus is thought to confer lifelong protection, some of the patient's antibodies cross‐react with other flaviviruses without cross‐neutralizing. The original antigenic sin phenomenon may amplify such antibodies upon subsequent heterologous flavivirus infection, potentially aggravating disease by antibody‐dependent enhancement (ADE). The most striking example is provided by the four different dengue viruses, where infection by one serotype appears to predispose to more severe disease upon infection by a second one. A similar effect was postulated for sequential infections with Zika and dengue viruses. In this review, we analyze the molecular determinants of the dual antibody response to flavivirus infection or vaccination in humans. We highlight the role of conserved partially cryptic epitopes giving rise to cross‐reacting and poorly neutralizing, ADE‐prone antibodies. We end by proposing a strategy for developing an epitope‐focused vaccine approach to avoid eliciting undesirable antibodies while focusing the immune system on producing protective antibodies only.