Provided the right hydrophilic/hydrophobic balance can be achieved, amphiphilic block copolymers are able to assemble in water into membranes. These membranes can enclose forming spheres with an aqueous core. Such structures, known as polymer vesicles or polymersomes (from the Greek “-some” = “body of”), have sizes that vary from tens to thousands of nanometers. The wholly synthetic nature of block copolymers affords control over parameters such as the molar mass and composition which ultimately determine the structure and properties of the species in solution. By varying the copolymer molecular mass it is possible to adjust the mechanical properties and permeability of the polymersomes, while the synthetic nature of copolymers allows the design of interfaces containing various biochemically-active functional groups. In particular, non-fouling and non-antigenic polymers have been combined with hydrophobic polymers in the design of biocompatible nano-carriers that are expected to exhibit very long circulation times. Stimulus-responsive block copolymers have also been used to exploit the possibility to trigger the disassembly of polymersomes in response to specific external stimuli such as pH, oxidative species, and enzyme degradation. Such bio-inspired ‘bottom-up’ supramolecular design principles offer outstanding advantages in engineering structures at a molecular level, using the same long-studied principles of biological molecules. Thanks to their unique properties, polymersomes have already been reported and studied as delivery systems for both drugs, genes, and image contrast agents as well as nanometer-sized reactors.