Antibodies that neutralize diverse strains of HIV-1 develop in ∼20% of HIV-1-infected individuals, and isolation and structural characterization of these antibodies are revealing how they recognize the envelope glycoprotein spike. Broadly reactive neutralizing antibodies utilize just a few sites of spike vulnerability and converge on select modes of recognition. These antibodies have unusual features: uncommonly long complementarity-determining loops, extensive somatic mutation, or both. Recent advances in next-generation sequencing of antibody-gene transcripts are providing genetic records of the development of neutralizing antibodies. These records inform an understanding of the naive B cell repertoire, of somatic mutation, and of the resulting antibody features that are critical to effective HIV-1 neutralization; based on these, we propose an ontogeny and structure-based system of antibody classification. The human immune system is capable of developing antibodies that broadly neutralize HIV-1—and an increasingly detailed view is accumulating for how effective immunity against HIV-1 can be generated.