The recent pandemic caused by the novel human coronavirus, referrred to as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), not only is having a great impact on the health care systems and economies in all continents but it is also causing radical changes of common habits and life styles. The novel coronavirus (CoV) recognises, with high probability, a zoonotic origin but the role of animals in the SARS-CoV-2 epidemiology is still largely unknown. However, CoVs have been known in animals since several decades, so that veterinary coronavirologists have a great expertise on how to face CoV infections in animals, which could represent a model for SARS-CoV-2 infection in humans. In the present paper, we provide an up-to-date review of the literature currently available on animal CoVs, focusing on the molecular mechanisms that are responsible for the emergence of novel CoV strains with different antigenic, biologic and/or pathogenetic features. A full comprehension of the mechanisms driving the evolution of animal CoVs will help better understand the emergence, spreading, and evolution of SARS-CoV-2.