SARS-CoV-2 is a new human coronavirus (CoV). It emerged in China in late 2019 and is responsible for the global COVID-19 pandemic that caused more than 340,000 deaths in four months. Understanding the origin of this virus is an important issue and it is necessary to determine the mechanisms of its dissemination in order to contain future epidemics. Based on phylogenetic inferences, sequence analysis and structure-function relationships of coronavirus proteins, informed by the knowledge currently available on the virus, we discuss the different scenarios evoked to account for the origin - natural or synthetic - of the virus. Based on available data, it is currently impossible to firmly assert whether SARS-CoV2 results from a natural zoonotic emergence or from an accidental escape of a laboratory strain. Regardless of its origin, studying the evolution of the molecular mechanisms involved in the emergence of this pandemic virus is essential to develop therapeutic and vaccine strategies.