This paper discusses the significance of Additive manufacturing (AM) in biomedical engineering technology with special reference to artificial organs. Copolyester resorbable polymeric composites have opened new opportunities for using AM technology for the production of functional, biocompatible artificial organs according to individual patient needs. These materials can present a viable approach to fabricating scaffolds with similar mechanical characteristics and bio-degradable tissue properties. This paper concentrates on resorbable polymeric composites obtained from polylactic acid (PLA) and polycaprolactone (PCL) and blends based on these two polymers with bioactive reinforcing agents for constructing artificial organs. The tailored material property, namely stiffness and degradation rate, creates organs with opportunities for cellular growth, tissue formation, and then resorption following implantation without detrimental consequences. Additionally, the potential application of 3D printing technologies in improving the structural, geometrical, and functional accuracy of the organs is covered. The target realistic applications of additive manufacturing in developing functional artificial organs for transplantation, drug screening proof, and disease modeling are outlined with corresponding difficulties and potential developments as the research agenda for the fresh field of additive manufacturing.