Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the cause of the COVID-19 (coronavirus disease 2019) pandemic, is a positive strand RNA (+RNA) virus. Like other +RNA viruses, SARS-CoV-2 is dependent on host cell metabolic machinery to survive and replicate, remodeling cellular membranes to generate sites of viral replication. Viral RNA-containing double-membrane vesicles (DMVs) are a striking feature of +RNA viral replication and are abundant in SARS-CoV-2–infected cells. Their generation involves rewiring of host lipid metabolism, including lipid biosynthetic pathways. Viruses can also redirect lipids from host cell organelles; lipid exchange at membrane contact sites, where the membranes of adjacent organelles are in close apposition, has been implicated in the replication of several +RNA viruses. Here we review current understanding of DMV biogenesis. With a focus on the exploitation of contact site machinery by +RNA viruses to generate replication organelles, we discuss evidence that similar mechanisms support SARS-CoV-2 replication, protecting its RNA from the host cell immune response.