Dengue virus, a positive-sense RNA virus, is one of the major human pathogens transmitted by mosquitoes. However, no fully effective licensed dengue vaccines or therapeutics are currently available. Several potent neutralizing antibodies against DENV have been isolated from mice and humans, and the characterization of their properties by biochemical and biophysical methods have revealed important insights for development of therapeutic antibodies. In this review, we summarize recently reported antibody–antigen complex structures, their likely neutralization mechanisms and enhancement propensities, as well as their prophylactic and therapeutic capabilities in mouse models. This article forms part of a symposium on flavivirus drug discovery in the journal Antiviral Research.