Action structures have been proposed as an algebraic framework for models of concurrent behaviour. In this thesis, refinements of action structures are developed, providing an abstract treatment of the structural aspect of processes, as well as a setting in which to study their dynamics. Concrete models of concurrent computation such as Petri nets and the π-calculus have been cast as action structures in a uniform manner, giving rise to a concrete class of action structures, called action calculi. As a result, action calculi are here adopted as the point of departure towards an abstract algebraic treatment of process construction and concurrent computation. The refinement of action structures to control structures gives a semantic space for action calculi; and includes a semantic account of names, based around a semantic counterpart to the syntactic notion of free names called surface. Two variants of action calculi are explored in analogous fashion. Present in these variants are some intuitively appealing aspects, such as greater expressivity of dataflow; a semantic treatment of name hiding or restrictions; and, in one of the variants, garbage collection of restricted but unused names and characterisations of surface in terms of restriction. While the treatment of process constructors reveals rich structural issues, the algebraic framework given by control structures provides considerable support for studying the dynamical aspects of processes. In particular, it allows a comparison of diverse action calculi upon their dynamic properties; illustrated here is a method achieving this. The method involves an examination of action calculi dynamics through the images of the calculi on a common static model called a classifier.