Cell membranes are essential barriers in Nature. To understand their properties and functions and to develop desirable applications, a simple and elegant approach is to study membranes that mimic the cell membrane. Lipid bilayers represent simple models that are physiologically representative when in the form of mixtures of various lipids, but they are not adequately stable even when covered with amphipathic proteins or when combined with polymers, thus preventing technological applications. This makes necessary the design of completely synthetic membranes. In this respect, amphiphilic copolymers that self‐assemble under dilute aqueous conditions and generate supramolecular polymer vesicles or films are ideal candidates for synthetic membranes. Their versatility in terms of chemistry and properties (permeability, mechanical stability, thickness), if appropriately designed, enable the insertion of biological molecules, such as membrane proteins and biopores, or the attachment of biomolecules at their surfaces. Here, we present the domain of synthetic membranes based on amphiphilic copolymers beginning with their generation and up to their applications in medicine, the food industry, and technology. Even though significant progress has been made in combining them with membrane proteins, open questions remain with respect to desired properties that could accommodate biological molecules and support further development of the field, from both the point of view of fundamental understanding and of applications. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012