Fused filament fabrication (FFF) is a 3D printing technique which allows layer-by-layer build-up of a part by the deposition of thermoplastic material through a nozzle. The technique allows for complex shapes to be made with a degree of design freedom unachievable with traditional manufacturing methods. However, the mechanical properties of the thermoplastic materials used are low compared to common engineering materials. In this work, composite 3D printing feedstocks for FFF are investigated, wherein carbon fibres are embedded into a thermoplastic matrix to increase strength and stiffness. First, the key processing parameters for FFF are reviewed, showing how fibres alter the printing dynamics by changing the viscosity and the thermal profile of the printed material. The state-of-the-art in composite 3D printing is presented, showing a distinction between short fibre feedstocks versus continuous fibre feedstocks. An experimental study was performed to benchmark these two methods. It is found that printing of continuous carbon fibres using the MarkOne printer gives significant increases in performance over unreinforced thermoplastics, with mechanical properties in the same order of magnitude of typical unidirectional epoxy matrix composites. The method, however, is limited in design freedom as the brittle continuous carbon fibres cannot be deposited freely through small steering radii and sharp angles. Filaments with embedded short carbon microfibres (∼100 μm) show better print capabilities and are suitable for use with standard printing methods, but only offer a slight increase in mechanical properties over the pure thermoplastic properties. It is hypothesized that increasing the fibre length in short fibre filament is expected to lead to increased mechanical properties, potentially approaching those of continuous fibre composites, whilst keeping the high degree of design freedom of the FFF process.