Key Points Plus-stranded RNA viruses induce large membrane structures that might support the replication of their genomes. Similarly, cytoplasmic replication of poxviruses (large DNA viruses) occurs in associated membranes. These membranes originate from the endoplasmic reticulum (ER) or endosomes. Membrane vesicles that support viral replication are induced by a number of RNA viruses. Similarly, the poxvirus replication site is surrounded by a double-membraned cisterna that is derived from the ER. Analogies to autophagy have been proposed since the finding that autophagy cellular processes involve the formation of double-membrane vesicles. However, molecular evidence to support this hypothesis is lacking. Membrane association of the viral replication complex is mediated by the presence of one or more viral proteins that contain sequences which associate with, or integrate into, membranes. Replication-competent membranes might contain viral or cellular proteins that contain amphipathic helices, which could mediate the membrane bending that is required to form spherical vesicles. Whereas poxvirus DNA replication occurs inside the ER-enclosed site, for most RNA viruses the topology of replication is not clear. Preliminary results for some RNA viruses suggest that their replication could also occur inside double-membrane vesicles. We speculate that cytoplasmic replication might occur inside sites that are 'enwrapped' by an ER-derived cisterna, and that these cisternae are open to the cytoplasm. Thus, RNA and DNA viruses could use a common mechanism for replication that involves membrane wrapping by cellular cisternal membranes. We propose that three-dimensional analyses using high-resolution electron-microscopy techniques could be useful for addressing this issue. High-throughput small-interfering-RNA screens should also shed light on molecular requirements for virus-induced membrane modifications.