Vesicles are self‐supported closed bilayer assemblies of amphiphiles that enclose an aqueous interior volume. The most important vesicle‐forming amphiphiles are phospholipids forming
liposomes
, as well as amphiphilic block copolymers forming
polymersomes
. Vesicles are investigated with respect to biomedical and cosmetic applications. The article covers energy and kinetic aspects of bilayer and vesicle formation, vesicle preparation methods, classification of vesicle shapes and shape transitions, mechanical properties of vesicle membranes, methods to improve vesicle stability, and biomedical aspects such as loading and sustained or triggered release of encapsulants, reconstitution of membrane proteins, and cell adhesion. An overview of all vesicle‐forming polymers is given. Theoretical concepts such as curvature and elasticity energy are introduced and their consequence for vesicle formation, size, and shape are discussed.