Worldwide SARS-CoV-2 transmission leads to the recurrent emergence of variants, such as the recently described B.1.617.1 (kappa), B.1.617.2 (delta) and B.1.617.2+ (delta+). The B.1.617.2 (delta) variant of concern is causing a new wave of infections in many countries, mostly affecting unvaccinated individuals, and has become globally dominant. We show that these variants dampen the in vitro potency of vaccine-elicited serum neutralizing antibodies and provide a structural framework for describing the impact of individual mutations on immune evasion. Mutations in the B.1.617.1 (kappa) and B.1.617.2 (delta) spike glycoproteins abrogate recognition by several monoclonal antibodies via alteration of key antigenic sites, including an unexpected remodeling of the B.1.617.2 (delta) N-terminal domain. The binding affinity of the B.1.617.1 (kappa) and B.1.617.2 (delta) receptor-binding domain for ACE2 is comparable to the ancestral virus whereas B.1.617.2+ (delta+) exhibits markedly reduced affinity. We describe a previously uncharacterized class of N-terminal domain-directed human neutralizing monoclonal antibodies cross-reacting with several variants of concern, revealing a possible target for vaccine development.