Phospholipids self-assemble in solution as fluid bilayers of typically 5 nm thickness, leading to lamellae structures of planar, cylindrical, spherical or even more complex geometries. When the bilayers enclose an inner spherical or cylindrical space one refers to these assemblies as vesicles or liposomes. In the living realm, where phospholipid bilayers build the walls of cells and cellular organelles, vesicles and liposomes provide simple models to understand cell wall properties: transport, fusion, mechanical resistance... Depending on the actual self-assembly conditions, single or multiple layer vesicles can be prepared in a large size range, from liposomes as small as a few tens of nanometers to giant unilamellar vesicles (GUVs) as large as one tenth of a millimetre. Following seminal work by Helfrich, who first recognized the importance of the membrane bending elasticity, extensive theoretical and experimental studies contributed to the writing of one of the finest chapters in modern statistical physics of soft condensed matter. Interestingly, fluid bilayers also inspired many fundamental studies in Mathematics, particularly in topology and differential geometry, some of these studies bearing a direct impact on the physical description of the membranes. Research in the field of two-dimensional lipid assembly is now opening exciting new perspectives towards many new directions, an effort that we are proud to join and keen to contribute to.