Since the appearance of the first cases of COVID-19 in 2019, an unprecedented number of documents on that disease have been published in a short space of time. The current available information covers a large number of topics related with COVID-19 and/or the coronavirus (SARS-CoV-2) responsible of the disease. However, only a limited number of publications have been focused on a controversial issue: the origin of the SARS-CoV-2. In this paper, the scientific literature on the origin of SARS-CoV-2 has been reviewed. Documents published during 2020 and 2021 (January 1-July 19) in journals that are indexed in PubMed and/or Scopus has been considered. The revised studies were grouped according to these two potential origins: natural and unnatural. The analyses of the conclusions of the different documents here assessed show that even considering the zoonotic hypothesis as the most likely, with bats and pangolins being possibly in the origin of the coronavirus, today's date the intermediate source species of SARS-CoV-2 has not been confirmed yet. On the other hand, some researchers point to an unnatural origin of this coronavirus, but their conclusions are not strongly supported by a clear scientific evidence. Given the tremendous severity of the current pandemic, investigations to establish clearly and definitively the origin of SARS-CoV-2, are basic and essential in order to prevent potential future pandemics of similar nature.