Three-dimensional (3D) printing has been successfully applied for the fabrication of polymer components ranging from prototypes to final products. An issue, however, is that the resulting 3D printed parts exhibit inferior mechanical performance to parts fabricated using conventional polymer processing technologies, such as compression moulding. The addition of fibres and other materials into the polymer matrix to form a composite can yield a significant enhancement in the structural strength of printed polymer parts. This review focuses on the enhanced mechanical performance obtained through the printing of fibre-reinforced polymer composites, using the fused filament fabrication (FFF) 3D printing technique. The uses of both short and continuous fibre-reinforced polymer composites are reviewed. Finally, examples of some applications of FFF printed polymer composites using robotic processes are highlighted.