The increase in the number of structural applications of composite materials, especially in the aerospace and automotive industries, has led to a demand for robust models to simulate composite forming processes. The mechanical behaviour of composite materials during forming is relatively complex due to their fibre-matrix composition. Many research studies have been conducted in the past 25-plus years into experimental methods for the characterization of the mechanical behaviours that are exhibited by textile-reinforced composite material systems during forming and into the development of material models to be used in computer codes for forming simulations. These studies have been presented and discussed in the ESA-FORM conferences since 1997 and especially in the 'Composite Forming Processes' mini-symposium launched in 2001. This article presents a survey of the research carried out in this context. Mechanical characterization tests specific to composite forming are presented as well as recent analysis techniques such as digital image correlation and X-ray tomography. Threedimensional mechanical behaviour laws, in particular hypo-and hyperelastic, have been developed and extended to second gradient models. Specific shell approaches have been presented and their application to wrinkling analysis. Resin flow and permeability analysis is another area of research in composite forming processes which are discussed in this article. Research on certain processes is also presented, in particular thermoforming of thermoplastic composites, wet compression moulding, pultrusion, automated fibre placement and three-dimensional printing. This comprehensive review of the works of multiple research groups is a recognition of the breadth and depth of efforts that have been invested into the understanding of the manufacturability of textile-reinforced composite materials.