While the developments of additive manufacturing (AM) techniques have been remarkable thus far, they are still significantly limited by the range of printable, functional material systems that meet the requirements of a broad range of industries; including the healthcare, manufacturing, packaging, aerospace and automotive industries. Furthermore, with the rising demand for sustainable developments, this review broadly gives the reader a good overview of existing AM techniques; with more focus on the extrusion-based technologies (Fused Deposition Modelling and Direct Ink Writing) due to their scalability, cost-efficiency and wider range of material processability. It then goes on to identify the innovative materials and recent research activities that may support the sustainable development of extrusion-based techniques for functional and multifunctional (4D printing) part and product fabrication.