Highly effective prophylactic vaccines for flaviviruses including yellow fever virus, tick-borne encephalitis virus and Japanese encephalitis virus are currently in use. However, the development of a dengue virus (DENV) vaccine has been hampered by the requirement of simultaneous protection against four distinct serotypes and the threat that DENV-specific antibodies might either mediate neutralization or, on the contrary, exacerbate disease through the phenomenon of antibody-dependent enhancement (ADE) of infection. Therefore, understanding the cellular, biochemical and molecular basis of antibody-mediated neutralization and ADE are fundamental for the development of a safe DENV vaccine. Here we summarize current structural and mechanistic knowledge underlying these phenomena. We also review recent results demonstrating that the humoral immune response triggered during natural DENV infection is able to generate neutralizing antibodies binding complex quaternary epitopes only present on the surface of intact virions.