Additive manufacturing (AM, aka 3D printing) is generally acknowledged as a “green” technology. However, its wider uptake in industry largely relies on the development of composite feedstock for imparting superior mechanical properties and bespoke functionality. Composite materials are especially needed in polymer AM, given the otherwise poor performance of most polymer parts in load-bearing applications. As a drawback, the shift from mono-material to composite feedstock may worsen the environmental footprint of polymer AM. This perspective aims to discuss this chasm between the advantage of embedding advanced functionality, and the disadvantage of causing harm to the environment. Fused filament fabrication (FFF, aka fused deposition modelling, FDM) is analysed here as a case study on account of its unparalleled popularity. FFF, which belongs to the material extrusion (MEX) family, is presently the most widespread polymer AM technique for industrial, educational, and recreational applications. On the one hand, the FFF of composite materials has already transitioned “from lab to fab” and finally to community, with far-reaching implications for its sustainability. On the other hand, feedstock materials for FFF are thermoplastic-based, and hence highly amenable to recycling. The literature shows that recycled thermoplastic materials such as poly(lactic acid) (PLA), acrylonitrile-butadiene-styrene (ABS), and polyethylene terephthalate (PET, or its glycol-modified form PETG) can be used for printing by FFF, and FFF printed objects can be recycled when they are at the end of life. Reinforcements/fillers can also be obtained from recycled materials, which may help valorise waste materials and by-products from a wide range of industries (for example, paper, food, furniture) and from agriculture. Increasing attention is being paid to the recovery of carbon fibres (for example, from aviation), and to the reuse of glass fibre-reinforced polymers (for example, from end-of-life wind turbines). Although technical challenges and economical constraints remain, the adoption of recycling strategies appears to be essential for limiting the environmental impact of composite feedstock in FFF by reducing the depletion of natural resources, cutting down the volume of waste materials, and mitigating the dependency on petrochemicals.