Emerging SARS-CoV-2 strains, B.1.1.7 and B.1.351, from the UK and South Africa, respectively show decreased neutralization by monoclonal antibodies and convalescent or vaccinee sera raised against the original wild-type virus, and are thus of clinical concern. However, the neutralization potency of two antibodies, 1-57 and 2-7, which target the receptor-binding domain (RBD) of spike, was unaffected by these emerging strains. Here, we report cryo-EM structures of 1-57 and 2-7 in complex with spike, revealing each of these antibodies to utilize a distinct mechanism to bypass or accommodate RBD mutations. Notably, each antibody represented a response with recognition distinct from those of frequent antibody classes. Moreover, many epitope residues recognized by 1-57 and 2-7 were outside hotspots of evolutionary pressure for both ACE2 binding and neutralizing antibody escape. We suggest the therapeutic use of antibodies like 1-57 and 2-7, which target less prevalent epitopes, could ameliorate issues of monoclonal antibody escape.