Semisolid processing of metallic alloys and composites utilises the thixotropic behaviour of materials with non-dendritic microstructure in the semisolid state. The family of innovative manufacturing methods based on this behaviour has been developing over the last 20 years or so and originates from scientific work at MIT in the early 1970s. Here, a summary is given of: routes to spheroidal microstructures; types of semisolid processing; and advantages and disadvantages of these routes. Background rheology and mathematical theories of thixotropy are then covered as precursors to the main focus of the review on transient behaviour of semisolid alloy slurries and computational modelling. Computational fluid dynamics (CFD) can be used to predict die filling. However, some of the reported work has been based on rheological data obtained in steady state experiments, where the semisolid material has been maintained at a particular shear rate for some time. In reality, in thixoforming, the slurry undergoes a sudden increase in shear rate from rest to 100 s(-1) or more as it enters the die. This change takes place in less than a second. Hence, measuring the transient rheological response under rapid changes in shear rate is critical to the development of modelling of die filling and successful die design for industrial processing. The modelling can be categorised as one-phase or two-phase and as finite difference or finite element. Recent work by Alexandrou and coworkers and, separately Modigell and coworkers, has led to the production of maps which, respectively summarise regions of stable/unstable flow and regions of laminar/transient/turbulent fill. These maps are of great potential use for the prediction of appropriate process parameters and avoidance of defects. A novel approach to modelling by Rouff and coworkers involves micro-modelling of the 'active zone' around spheroidal particles. There is little quantitative data on the discrepancies or otherwise between die fill simulations and experimental results (usually obtained through interrupted filling). There are no direct comparisons of the capabilities of various software packages to model the filling of particular geometries accurately. In addition, the modelling depends on rheological data and this is sparse, particularly for the increasingly complex two-phase models. Direct flow visualisation can provide useful insight and avoid the effects of inertia in interrupted filling experiments. (C) 2004 Elsevier Ltd. All rights reserved.