Positive-sense RNA ((+)RNA) viruses such as hepatitis C virus exploit host cells by subverting host proteins, remodelling subcellular membranes, co-opting and modulating protein and ribonucleoprotein complexes, and altering cellular metabolic pathways during infection. To facilitate RNA replication, (+)RNA viruses interact with numerous host molecules through protein-protein, RNA-protein and protein-lipid interactions. These interactions lead to the formation of viral replication complexes, which produce new viral RNA progeny in host cells. This Review presents the recent progress that has been made in understanding the role of co-opted host proteins and membranes during (+)RNA virus replication, and discusses common themes employed by different viruses.