The emergence of the coronavirus disease 2019 (COVID-19) caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) inspired rapid research efforts targeting the host range, pathogenesis and transmission mechanisms, and the development of antiviral strategies. Genetically modified mice, rhesus macaques, ferrets, and Syrian golden hamsters have been frequently used in studies of pathogenesis and efficacy of antiviral compounds and vaccines. However, alternatives to in vivo experiments, such as immortalized cell lines, primary respiratory epithelial cells cultured at an air–liquid interface, stem/progenitor cell-derived organoids, or tissue explants, have also been used for isolation of SARS-CoV-2, investigation of cytopathic effects, and pathogen–host interactions. Moreover, initial proof-of-concept studies for testing therapeutic agents can be performed with these tools, showing that animal-sparing cell culture methods could significantly reduce the need for animal models in the future, following the 3R principles of replace, reduce, and refine. So far, only few studies using animal-derived primary cells or tissues have been conducted in SARS-CoV-2 research, although natural infection has been shown to occur in several animal species. Therefore, the need for in-depth investigations on possible interspecies transmission routes and differences in susceptibility to SARS-CoV-2 is urgent. This review gives an overview of studies employing alternative culture systems like primary cell cultures, tissue explants, or organoids for investigations of the pathophysiology and reverse zoonotic potential of SARS-CoV-2 in animals. In addition, future possibilities of SARS-CoV-2 research in animals, including previously neglected methods like the use of precision-cut lung slices, will be outlined.