Biopolymers are promising environmentally benign materials applicable in multifarious applications. They are especially favorable in implantable biomedical devices thanks to their excellent unique properties, including bioactivity, renewability, bioresorbability, biocompatibility, biodegradability and hydrophilicity. Additive manufacturing (AM) is a flexible and intricate manufacturing technology, which is widely used to fabricate biopolymer-based customized products and structures for advanced healthcare systems. Three-dimensional (3D) printing of these sustainable materials is applied in functional clinical settings including wound dressing, drug delivery systems, medical implants and tissue engineering. The present review highlights recent advancements in different types of biopolymers, such as proteins and polysaccharides, which are employed to develop different biomedical products by using extrusion, vat polymerization, laser and inkjet 3D printing techniques in addition to normal bioprinting and four-dimensional (4D) bioprinting techniques. This review also incorporates the influence of nanoparticles on the biological and mechanical performances of 3D-printed tissue scaffolds. This work also addresses current challenges as well as future developments of environmentally friendly polymeric materials manufactured through the AM techniques. Ideally, there is a need for more focused research on the adequate blending of these biodegradable biopolymers for achieving useful results in targeted biomedical areas. We envision that biopolymer-based 3D-printed composites have the potential to revolutionize the biomedical sector in the near future.