Viruses are obligatory intracellular parasites and utilize host elements to support key viral processes, including penetration of the plasma membrane, initiation of infection, replication, and suppression of the host's antiviral defenses. In this review, we focus on picornaviruses, a family of positive-strand RNA viruses, and discuss the mechanisms by which these viruses hijack the cellular machinery to form and operate membranous replication complexes. Studies aimed at revealing factors required for the establishment of viral replication structures identified several cellular-membrane-remodeling proteins and led to the development of models in which the virus used a preexisting cellular-membrane-shaping pathway "as is" for generating its replication organelles. However, as more data accumulate, this view is being increasingly questioned, and it is becoming clearer that viruses may utilize cellular factors in ways that are distinct from the normal functions of these proteins in uninfected cells. In addition, the proteincentric view is being supplemented by important new studies showing a previously unappreciated deep remodeling of lipid homeostasis, including extreme changes to phospholipid biosynthesis and cholesterol trafficking. The data on viral modifications of lipid biosynthetic pathways are still rudimentary, but it appears once again that the viruses may rewire existing pathways to generate novel functions. Despite remarkable progress, our understanding of how a handful of viral proteins can completely overrun the multilayered, complex mechanisms that control the membrane organization of a eukaryotic cell remains very limited.