Immediately from the outset of the COVID-19 pandemic, researchers from diverse biomedical and biological disciplines have united to study the novel pandemic virus, SARS-CoV-2. The antibody response to SARS-CoV-2 has been a major focus of COVID-19 research due to its clinical relevance and importance in vaccine and therapeutic development. Isolation and characterization of antibodies to SARS-CoV-2 have been accumulating at an unprecedented pace. Most of the SARS-CoV-2 neutralizing antibodies to date target the spike (S) protein receptor binding domain (RBD), which engages the host receptor ACE2 for viral entry. Here we review the binding sites and molecular features of monoclonal antibodies that target the SARS-CoV-2 RBD, including a few that also cross-neutralize SARS-CoV.