Positive single-strand RNA (+ RNA) viruses can remodel host cell membranes to induce a replication organelle (RO) isolating the replication of their genome from innate immunity mechanisms. Some of these viruses, including severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2), induce double-membrane vesicles (DMVs) for this purpose. Viral non-structural proteins are essential for DMV biogenesis, but they cannot form without an original membrane from a host cell organelle and a significant supply of lipids. The endoplasmic reticulum (ER) and the initial mechanisms of autophagic processes have been shown to be essential for the biogenesis of SARS-CoV-2 DMVs. However, by analogy with other DMV-inducing viruses, it seems likely that the Golgi apparatus, mitochondria and lipid droplets are also involved. As for hepatitis C virus (HCV), pores crossing both membranes of SARS-CoV-2-induced DMVs have been identified. These pores presumably allow the supply of metabolites essential for viral replication within the DMV, together with the export of the newly synthesized viral RNA to form the genome of future virions. It remains unknown whether, as for HCV, DMVs with open pores can coexist with the fully sealed DMVs required for the storage of large amounts of viral RNA. Interestingly, recent studies have revealed many similarities in the mechanisms of DMV biogenesis and morphology between these two phylogenetically distant viruses. An understanding of the mechanisms of DMV formation and their role in the infectious cycle of SARS-CoV-2 may be essential for the development of new antiviral approaches against this pathogen or other coronaviruses that may emerge in the future.