Broadly neutralizing antibodies represent the major protective mechanism of vaccines targeting pathogenic microbes in humans and animals. For HIV, broadly neutralizing antibodies have also been shown to be protective in experimental animal models. However, despite the identification of a respectable number of broadly neutralizing antibodies from chronically infected HIV-positive persons in recent years, attempts to induce such antibodies by vaccines have generally failed over the last decades. Though unsuccessful in view of achieving a protective vaccine against HIV, many of these studies have contributed significantly to the understanding of the generation of broadly neutralizing antibodies against HIV-1 as well as to the vulnerable sites they target on the surface of the virus. Here we review the most important features of patient-derived broadly neutralizing antibodies, the long and complex B-cell maturation pathways required for their production, and the resulting consequences for vaccine development. We further address characteristics of the epitopes targeted by broadly neutralizing antibodies on the virus surface as well as mechanisms of viral escape. Taken together, the identification of vaccine candidates able to induce broadly neutralizing antibodies against HIV-1 is the major challenge in HIV vaccine development. Mutual coevolution of rationally designed HIV vaccine candidates, with affinity maturation pathways of antibodies they induce upon vaccination, may best mimic the natural situation of chronically HIV-infected patients who are able to generate broadly neutralizing antibodies.