The research community is in a race to understand the molecular mechanisms of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, to repurpose currently available antiviral drugs and to develop new therapies and vaccines against coronavirus disease 2019 (COVID-19). One major challenge in achieving these goals is the paucity of suitable preclinical animal models. Mice constitute ~70% of all the laboratory animal species used in biomedical research. Unfortunately, SARS-CoV-2 infects mice only if they have been genetically modified to express human ACE2. The inherent resistance of wild-type mice to SARS-CoV-2, combined with a wealth of genetic tools that are available only for modifying mice, offers a unique opportunity to create a versatile set of genetically engineered mouse models useful for COVID-19 research. We propose three broad categories of these models and more than two dozen designs that may be useful for SARS-CoV-2 research and for fighting COVID-19.