At present, most carbon fibres are used as reinforcement for polymers. Fabrication technologies for carbon-fibre-reinforced polymers (CFRPs) are now reaching a mature state that effectively replaces metals in various technical fields, including aerospace, sporting equipment, civil engineering, etc. However, there are many structures in which metal alloys cannot be replaced with CFRPs because of, firstly, the limited temperatures that plastics can survive, and secondly, the relatively low fracture toughness of CFRPs. This has led researchers to develop carbon-fibre/metal-matrix composites (CFMMCs), considering aluminium, titanium, and nickel alloys as potential matrix materials. The present paper presents a review of the corresponding results, focusing on those obtained in the current century.