Modelling of microstructure evolution has long been part of physical metallurgy, both in the laboratory and in industry. Until recently, however, physically-based modelling was limited to idealised alloys under controlled laboratory conditions, while the complexity of industrial processing of commercial alloys necessitated empirical approaches. The advent of powerful computing facilities, and in particular the rapid growth in application of the finite element method to metals processing, has stimulated new research with the aim of bringing the two areas together. The present review describes progress in this rapidly expanding field. The preliminary review in Section I illustrates the potential of integrating microstructural modelling with the very detailed process histories which are available from modern finite element analyses. The 'internal state variable' approach is identified as a particularly appropriate method to reach the objective of providing useful predictive capability in industrial processing, within the scope of personal computers. The general method, and its simplification for single parameter models in which the microstructure evolution may be treated as an 'isokinetic' reaction, are outlined in Section 2. The paper then presents internal state variable formulations for a range of thermal problems, as temperature-controlled processes dominate. These are solid-state diffusional transformations (precipitate dissolution, nucleation and growth, and coarsening) in Section 3; solidification and subsequent solid-state phase transformations in Section 4; and grain growth in Section 5. Case studies are presented for each problem, illustrating the applicability of the approach to industrially relevant processing of commercial alloys. Examples range from casting, to cooling after hot forming, to heat treatment and welding. Bringing together this range of phenomena and processes in one review makes two specific points: (a) the state variable formulation offers a robust modelling framework, in which real non-isothermal process histories may be readily linked to fundamental isothermal theories of microstructure evolution, (b) depending on the problem, different levels of approximation can be accepted without invalidatin 'a the results, but the modeller needs to exercise critical judgement to find the optimum level of complexity. Finally in Section 6, a number of examples are presented in which state variable models have been fully integrated with finite element analyses, with two examples from welding and one from casting. These case studies demonstrate that significant opportunities now exist for enhancing industrial processing capabilities. At the same time, the underlying microstructural modelling provides a renewed stimulus for improving scientific understanding of some of the classical problems of physical metallurgy. (C) 2002 Elsevier Science Ltd. All rights reserved.