Friction stir welding (FSW) has moved in one decade from its invention at TWI to large-scale commercial application, particularly for structural aluminium alloys. The process works by traversing a rotating profiled tool along the joint line, which simultaneously heats and deforms the material to form a solid-state weld. Process developments to date have been largely empirical, addressing parameters such as tool design, optimal traverse and rotation speed, and vertical force, for all major classes of alloys. Mechanical property and microstructure characterisation are most developed for FSW of aluminium alloys, often in comparison with arc welding. Activity in process modelling has lagged behind empirical process development, but has much to offer. There is as yet no consensus on how the process works in detail, so modelling can provide scientific understanding of the mechanisms and physical limits of the process. It is known that tool design is critical. and this presents the most demanding modelling challenge. At a simpler level modelling can also be used to accelerate trials, by predicting likely operating conditions in new materials or joint geometries. Of particular importance are predictions which guide designers in estimating the process economics, or establishing the performance of FSW joints: examples are the maximum process, speed for a given material and thickness, the avoidance of voids and defects, and the extent of microstructural (and property) change in the deformed and heat-affected regions. FSW presents an interesting modelling challenge, since it combines closely coupled heat flow, plastic deformation and microstructure evolution. All three contribute to a material's processability by FSW, and to the subsequent properties of the weld. A full mathematical description of the process needs to draw on modelling of both welding and hot deformation processes. This paper discusses the status of understanding of the friction stir process and the range of related modelling activity, both analytical and numerical. The main aspects covered are: (a) metal flow and friction below the tool; (b) the consequent. heat generation and the transient thermal field; (c) microstructure and property evolution, within the deformation zone and in the HAZ.