The emergence and global spread of COVID-19, an infectious disease caused by the novel coronavirus SARS-CoV-2, has resulted in a continuing pandemic threat to global health. Nuclear medicine techniques can be used for functional imaging of (patho)physiological processes at the cellular or molecular level and for treatment approaches based on targeted delivery of therapeutic radionuclides. Ongoing development of radiolabeling methods has significantly improved the accessibility of radiopharmaceuticals for in vivo molecular imaging or targeted radionuclide therapy, but their use for biosafety threats such as SARS-CoV-2 is restricted by the contagious nature of these agents. Here, we highlight several potential uses of nuclear medicine in the context of SARS-CoV-2 and COVID-19, many of which could also be performed in laboratories without dedicated containment measures. In addition, we provide a broad overview of experimental or repurposed SARS-CoV-2-targeting drugs and describe how radiolabeled analogs of these compounds could facilitate antiviral drug development and translation to the clinic, reduce the incidence of late-stage failures and possibly provide the basis for radionuclide-based treatment strategies. Based on the continuing threat by emerging coronaviruses and other pathogens, it is anticipated that these applications of nuclear medicine will become a more important part of future antiviral drug development and treatment.