The ongoing COVID-19 pandemic continues to affect the lives, wellbeing, and stability of communities worldwide. The race to save human lives is critical, and the development of useful translational animal models to elucidate disease pathogenesis and prevention, and to test therapeutic interventions, is essential to this response. However, significant limitations exist with the currently employed animal models that slow our ability to respond to the pandemic. Non-human primates serve as an excellent animal model for SARS-CoV-2 disease and interventions, but the availability of these animals is scarce, and few facilities are able to house and utilize this model. Adapted murine models are accessible and improving but lack natural hACE-2 receptors and are only moderate representatives of human COVID-19 disease, transmission, and immune responses. On the other hand, there are several animal species that are both naturally and experimentally infected, such as domestic cats, hamsters, ferrets, and mink. Several of these have proven animal-to-animal transmission and evidence of significant clinical and histopathologic disease that mimics acute COVID-19 in humans. Mobilizing these nontraditional animal models could have a crucial role in SARS-CoV-2 research efficiency and impact. This review focuses on what is known about these nontraditional animal models, including their immune responses to SARS-CoV-2 infection, evidence of clinical and histopathologic disease, transmission potential, and the practicality of each model in a research setting. Comparative insight into these animal models for COVID-19 can strengthen the efforts to mitigate this pandemic.