Vaccines that protect against viral infection usually elicit neutralizing antibodies, but HIV-1 vaccine candidates have failed to induce broad and potent such responses. Broadly active neutralizing antibodies (bNAbs) do, however, slowly emerge in a minority of HIV-1-infected subjects; and passive immunization with bNAbs protects against viral acquisition in animal models of HIV-1 infection. New techniques have made it possible to interrogate human B cells and thereby to isolate highly potent bNAbs to uncharted epitope clusters. Furthermore, recent high-resolution structure determinations of near-native soluble envelope glycoprotein trimers in complex with different bNAbs reveal the molecular basis for neutralization. Such trimer structures may serve as blueprints for vaccine design. Here we discuss how a vaccine might bridge a reactivity gap from germline antibody to bNAb and simulate the intricate stimuli of affinity maturation that sometimes prevail in chronic infection.