All single-stranded 'positive-sense' RNA viruses that infect mammalian, insect or plant cells rearrange internal cellular membranes to provide an environment facilitating virus replication. A striking feature of these unique membrane structures is the induction of 70-100 nm vesicles (either free within the cytoplasm, associated with other induced vesicles or bound within a surrounding membrane) harbouring the viral replication complex (RC). Although similar in appearance, the cellular composition of these vesicles appears to vary for different viruses, implying different organelle origins for the intracellular sites of viral RNA replication. Genetic analysis has revealed that induction of these membrane structures can be attributed to a particular viral gene product, usually a non-structural protein. This review will highlight our current knowledge of the formation and composition of virus RCs and describe some of the similarities and differences in RNA-membrane interactions observed between the virus families Flaviviridae and Picornaviridae.