SARS-CoV-2 is a new human coronavirus (CoV), which emerged in China in late 2019 and is responsible for the global COVID-19 pandemic that caused more than 59 million infections and 1.4 million deaths in 11 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. The data currently available is not sufficient to firmly assert whether SARS-CoV2 results from a zoonotic emergence or from an accidental escape of a laboratory strain. This question needs to be solved because it has important consequences on the evaluation of risk/benefit balance of our interaction with ecosystems, the intensive breeding of wild and domestic animals, as well as some lab practices and on scientific policy and biosafety regulations. Regardless of its origin, studying the evolution of the molecular mechanisms involved in the emergence of pandemic viruses is essential to develop therapeutic and vaccine strategies and to prevent future zoonoses. This article is a translation and update of a French article published in Médecine/Sciences, Aug/Sept 2020 (http://doi.org/10.1051/medsci/2020123).