The chemical vapour infiltration (CVI) process is used to fabricate the interphases and matrices of CMCs. This process involves complex physico-chemical phenomena such as the transport of precursor, carrier, and by-product gases in the reactor and inside a fibrous preform, chemical reactions (pyrolysis and deposition), and the structural evolution of the preform. It is able to provide high-quality materials because the process conditions are rather mild with respect to the fibres ; however it is expensive and sometimes difficult to optimize. Many variations of the basic concept have been proposed in the past decades, introducing thermal and pressure gradients, in order to increase the efficiency. This process has been the object of extensive modelling efforts, because of imperative optimization needs. The present work is an attempt to provide a synthetic view of these models, focusing on several features of CVI modelling : i) Modelling CVI requires a multi-scale strategy, with models ranging from process scale down to atomic scale, ii) Original physicochemical couplings are involved, which require the development of adequate treatments, iii) There is a hierarchy of model refinement, ranging from fully detailed models to quasi-analytical predictions.