We present the ß-calculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The calculus is an extension of the process algebra CCS, following work by Engberg and Nielsen who added mobility to CCS while preserving its algebraic properties. The ß-calculus gains simplicity by removing all distinction between variables and constants; communication links are identified by names, and computation is represented purely as the communication of names across links. After an illustrated description of how the ß-calculus generalises conventional process algebras in treating mobility, several examples exploiting mobility are given in some detail. The important examples are the encoding into the ß- calculus of higher-order functions (the -calculus and combinatory algebra), the tr...