Pultrusion is in principle a simple process which is used to manufacture constant cross-sectional fibre-reinforced polymer composites. The process has a low labour requirement and a high raw material conversion efficiency as it is a continuous processing technique. Even if the pultrusion process is conceptually quite simple, the analysis of its physics, dynamics and definition of optimal processing parameters, are complex tasks. Keeping in mind the multiphysics and large amount of variables involved in the pultrusion process, a satisfactory experimental analysis of this production process requires considerable time, which is obviously not a cost-efficient approach. In order to avoid the expensive trial-and-error approaches for designing new products and optimising process conditions, the development of computational process models is crucial. This update focuses on the numerical modelling of pultrusion processes. State-of-the-art process models are reviewed and the governing principles are explained in a systematic way. The main challenges faced during pultrusion, such as process-induced residual stresses, shape distortions, thermal history, species conversion, phase changes, impregnation of the reinforcements and pulling force, are described and related examples are provided. Moreover, the strategies for obtaining a reliable and optimised process using probabilistic approaches and optimisation algorithms are summarised. One focus of this update is the thermochemical and mechanical analyses of the pultrusion process for industrial profiles, such as a rectangular box section, L-shaped profile, I-beam, and flat and round profiles, in which the process-induced stresses and dimensional variations together with the thermal and cure developments are highlighted.