The ongoing pandemic of coronavirus disease 2019 (COVID-19), which is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a major threat to global health and the medical countermeasures available so far are limited^,. Moreover, we currently lack a thorough understanding of the mechanisms of humoral immunity to SARS-CoV-2. Here we analyse a large panel of human monoclonal antibodies that target the spike (S) glycoprotein, and identify several that exhibit potent neutralizing activity and fully block the receptor-binding domain of the S protein (S_RBD) from interacting with human angiotensin-converting enzyme 2 (ACE2). Using competition-binding, structural and functional studies, we show that the monoclonal antibodies can be clustered into classes that recognize distinct epitopes on the S_RBD, as well as distinct conformational states of the S trimer. Two potently neutralizing monoclonal antibodies, COV2-2196 and COV2-2130, which recognize non-overlapping sites, bound simultaneously to the S protein and neutralized wild-type SARS-CoV-2 virus in a synergistic manner. In two mouse models of SARS-CoV-2 infection, passive transfer of COV2-2196, COV2-2130 or a combination of both of these antibodies protected mice from weight loss and reduced the viral burden and levels of inflammation in the lungs. In addition, passive transfer of either of two of the most potent ACE2-blocking monoclonal antibodies (COV2-2196 or COV2-2381) as monotherapy protected rhesus macaques from SARS-CoV-2 infection. These results identify protective epitopes on the S_RBD and provide a structure-based framework for rational vaccine design and the selection of robust immunotherapeutic agents.