To date severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has infected over 100 million individuals resulting in over two million deaths. Many vaccines are being deployed to prevent coronavirus disease 2019 (COVID-19) including two novel mRNA-based vaccines1,2. These vaccines elicit neutralizing antibodies and appear to be safe and effective, but the precise nature of the elicited antibodies is not known3–6. Here we report on the antibody and memory B cell responses in a cohort of 20 volunteers who received either the Moderna (mRNA-1273) or Pfizer-BioNTech (BNT162b2) vaccines. Consistent with prior reports, 8 weeks after the second vaccine injection volunteers showed high levels of IgM, and IgG anti-SARS-CoV-2 spike protein (S) and receptor binding domain (RBD) binding titers3,5,6. Moreover, the plasma neutralizing activity, and the relative numbers of RBD-specific memory B cells were equivalent to individuals who recovered from natural infection7,8. However, activity against SARS-CoV-2 variants encoding E484K or N501Y or the K417N:E484K:N501Y combination was reduced by a small but significant margin. Consistent with these findings, vaccine-elicited monoclonal antibodies (mAbs) potently neutralize SARS-CoV-2, targeting a number of different RBD epitopes in common with mAbs isolated from infected donors. Structural analyses of mAbs complexed with S trimer suggest that vaccine- and virus-encoded S adopts similar conformations to induce equivalent anti-RBD antibodies. However, neutralization by 14 of the 17 most potent mAbs tested was reduced or abolished by either K417N, or E484K, or N501Y mutations. Notably, the same mutations were selected when recombinant vesicular stomatitis virus (rVSV)/SARS-CoV-2 S was cultured in the presence of the vaccine elicited mAbs. Taken together the results suggest that the monoclonal antibodies in clinical use should be tested against newly arising variants, and that mRNA vaccines may need to be updated periodically to avoid potential loss of clinical efficacy.