Three-dimensional (3D) printing, known as the most promising approach for bioartificial organ manufacturing, has provided unprecedented versatility in delivering multi-functional cells along with other biomaterials with precise control of their locations in space. The constantly emerging 3D printing technologies are the integration results of biomaterials with other related techniques in biology, chemistry, physics, mechanics and medicine. Synthetic polymers have played a key role in supporting cellular and biomolecular (or bioactive agent) activities before, during and after the 3D printing processes. In particular, biodegradable synthetic polymers are preferable candidates for bioartificial organ manufacturing with excellent mechanical properties, tunable chemical structures, non-toxic degradation products and controllable degradation rates. In this review, we aim to cover the recent progress of synthetic polymers in organ 3D printing fields. It is structured as introducing the main approaches of 3D printing technologies, the important properties of 3D printable synthetic polymers, the successful models of bioartificial organ printing and the perspectives of synthetic polymers in vascularized and innervated organ 3D printing areas.