The severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) pandemic continues, with devasting consequences for human lives and the global economy^,. The discovery and development of virus-neutralizing monoclonal antibodies could be one approach to treat or prevent infection by this coronavirus. Here we report the isolation of sixty-one SARS-CoV-2-neutralizing monoclonal antibodies from five patients infected with SARS-CoV-2 and admitted to hospital with severe coronavirus disease 2019 (COVID-19). Among these are nineteen antibodies that potently neutralized authentic SARS-CoV-2 in vitro, nine of which exhibited very high potency, with 50% virus-inhibitory concentrations of 0.7 to 9 ng ml⁻¹. Epitope mapping showed that this collection of nineteen antibodies was about equally divided between those directed against the receptor-binding domain (RBD) and those directed against the N-terminal domain (NTD), indicating that both of these regions at the top of the viral spike are immunogenic. In addition, two other powerful neutralizing antibodies recognized quaternary epitopes that overlap with the domains at the top of the spike. Cryo-electron microscopy reconstructions of one antibody that targets the RBD, a second that targets the NTD, and a third that bridges two separate RBDs showed that the antibodies recognize the closed, ‘all RBD-down’ conformation of the spike. Several of these monoclonal antibodies are promising candidates for clinical development as potential therapeutic and/or prophylactic agents against SARS-CoV-2.