The field of additive manufacturing is rapidly growing that aims in the development of sophisticated construct for in vitro modeling and tissue regeneration, offering hope of bridging the gap between organ shortage and transplantation need. The recent advances in this field is the ability of printing biocompatible material and the most importantly to precisely dispense cell-laden biomaterials for the construction of complex 3D functional living tissues and organs. The field of bioprinting has laid a milestone in various disciplines such as tissue engineering, regenerative medicine and pharmaceutics. In particular, the creation of vascularized tissue remained a principle challenge in the field of tissue engineering. Compared to the non-biological printing such as the polymeric scaffold printing, the process of bioprinting involves a lot of complexities. Some of the critical challenges involve the type of material, cell, growth factor, cell viability and many more. These entanglements are being addressed by the amalgamation of different technologies like engineering, material science, cell biology, physics and medicine. Here we review on the advancement in the 3D bioprinting process and the commonly used material for bioprinting. We focus on the properties of an ideal bioink and the cell response to the printed scaffold. Finally, we conclude with the current challenges and the future perspective of 3D organ printing.