Although COVID-19 has only recently appeared, research studies have already developed and implemented many animal models for deciphering the secrets of the disease and provided insights into the biology of SARS-CoV-2. However, there are several major factors that complicate the study of this virus in model organisms, such as the poor infectivity of clinical isolates of SARS-CoV-2 in some model species, and the absence of a persistent infection, immunopathology, severe acute respiratory distress syndrome, and none of the systemic complications which characterize COVID-19 clinically. Another important limitation is that SARS-CoV-2 mainly causes severe COVID-19 in older people with comorbidities, which represents a serious problem when attempting to use young and immunologically naïve laboratory animals in COVID-19 testing. We review here the main animal models developed so far to study COVID-19 and the unique advantages of the zebrafish model that may help to contribute to understand this disease, in particular to the identification and repurposing of drugs to treat COVID-19, to reveal the mechanism of action and side-effects of Spike-based vaccines, and to decipher the high susceptibility of aged people to COVID-19.