In March 2020, the World Health Organization Department declared the coronavirus (COVID-19) outbreak a global pandemic, as a consequence of its rapid spread on all continents. The COVID-19 pandemic has been not only a health emergency but also a serious general problem as fear of contagion and severe restrictions put economic and social activity on hold in many countries. Considering the close link between human and animal health, COVID-19 might infect wild and companion animals, and spawn dangerous viral mutants that could jump back and pose an ulterior threat to us. The purpose of this review is to provide an overview of the pandemic, with a particular focus on the clinical manifestations in humans and animals, the different diagnosis methods, the potential transmission risks, and their potential direct impact on the human–animal relationship.