The continuous emergence of novel viruses and their diseases are a threat to global public health as there have been three outbreaks of coronaviruses that are highly pathogenic to humans in the span of the last two decades, severe acute respiratory syndrome (SARS)-CoV in 2002, Middle East respiratory syndrome (MERS)-CoV in 2012, and novel SARS-CoV-2 which emerged in 2019. The unprecedented spread of SARS-CoV-2 worldwide has given rise to multiple SARS-CoV-2 variants that have either altered transmissibility, infectivity, or immune escaping ability, causing diseases in a broad range of animals including human and non-human hosts such as companion, farm, zoo, or wild animals. In this review, we have discussed the recent SARS-CoV-2 outbreak, potential animal reservoirs, and natural infections in companion and farm animals, with a particular focus on SARS-CoV-2 variants. The expeditious development of COVID-19 vaccines and the advancements in antiviral therapeutics have contained the COVID-19 pandemic to some extent; however, extensive research and surveillance concerning viral epidemiology, animal transmission, variants, or seroprevalence in diverse hosts are essential for the future eradication of COVID-19.