Fibre metal laminates, hybrid composite materials built up from interlaced layers of thin metals and fibre reinforced adhesives, are future-proof materials used in the production of passenger aircraft, yachts, sailplanes, racing cars, and sports equipment. The most commercially available fibre–metal laminates are carbon reinforced aluminium laminates, aramid reinforced aluminium laminates, and glass reinforced aluminium laminates. This review emphasises the developing technologies for forming hybrid metal–polymer composites (HMPC). New advances and future possibilities in the forming technology for this group of materials is discussed. A brief classification of the currently available types of FMLs and details of their methods of fabrication are also presented. Particular emphasis was placed on the methods of shaping FMLs using plastic working techniques, i.e., incremental sheet forming, shot peening forming, press brake bending, electro-magnetic forming, hydroforming, and stamping. Current progress and the future directions of research on HMPCs are summarised and presented.