The SARS-CoV-2 virus’s prominence, severity, and unique characteristics—including its ability to mutate quickly and cause idiosyncratic symptoms—has prompted researchers to fully focus on understanding the pathological process behind infection and developing an effective vaccine. To achieve this objective, several animal models, from small animals to non-human primates (NHPs), have been developed to identify different immunizing agents, which can provide protection against coronavirus disease (COVID-19). In this review, we discuss the possible advantages and drawbacks of these animal models including their susceptibility to infection, and pathological manifestations. While vaccination efforts have been successful, there still remain several limitations and areas for improvement. The individuals at the high risk of contracting viral infection may need individualized immunization plans and newer antigenic targets must be discovered to combat the virus’s mutations. Animal models can serve as a valuable tool to develop better vaccines that can provide protection against COVID-19.