Curved aluminium alloy extrusion profiles have been widely used in many engineering applications due to their high-strength and high-stiffness to weight ratios. The curved extrusion profiles could be formed in several forming processes, such as roll-bending, stretch-bending and extrusion bending. This paper presents the review and analysis of their manufacturing processes and includes two parts. The first part is the review of manufacturing methods for producing curved extrusion components. The current cold bending processes can be grouped into three typical operations according to their characteristics, i.e., 2-point bending (cantilever bending), 3-point bending and stretch-bending. Key features of the operations, the main advantages, disadvantages and typical defects in the bending processes are summarised and analysed. The second part is the stress and strain analysis for the cold stretch-bending and pure bending of extrusion profiles. Particularly, the stress-strain distributions through the thickness of extrusion profiles, together with the neutral axis changes, are graphically illustrated and analysed. Further stress-strain analysis has been carried out on the “inner most” and “outer most” bending profile surfaces against the bending angle. Lastly, suggestions have been given on the future research directions, and the selection of the current existing processes for manufacturing defect free components.