Variable regions 1 and 2 (V1/V2) of human immunodeficiency virus-1 (HIV-1) gp120 envelope glycoprotein are critical for viral evasion of antibody neutralization, and are themselves protected by extraordinary sequence diversity and N-linked glycosylation. Human antibodies such as PG9 nonetheless engage V1/V2 and neutralize 80% of HIV-1 isolates. Here we report the structure of V1/V2 in complex with PG9. V1/V2 forms a four-stranded beta-sheet domain, in which sequence diversity and glycosylation are largely segregated to strand-connecting loops. PG9 recognition involves electrostatic, sequence-independent and glycan interactions: the latter account for over half the interactive surface but are of sufficiently weak affinity to avoid autoreactivity. The structures of V1/V2-directed antibodies CH04 and PGT145 indicate that they share a common mode of glycan penetration by extended anionic loops. In addition to structurally defining V1/V2, the results thus identify a paradigm of antibody recognition for highly glycosylated antigens, which-with PG9-involves a site of vulnerability comprising just two glycans and a strand.