Organ printing is defined as a computer-aided layer-by-layer additive robotic biofabrication of functional human 3D tissue and organ constructs using self-assembling tissue spheroids as building blocks. During last decade organ printing has been rapidly emerged as a potentially superior alternative of classic solid scaffold-based approach in tissue engineering. It is becoming increasingly obvious that organ printing could not be reduced anymore to just simple one step bioprinting process and it rather represents an integrated complex of enabling technologies which could be arranged into organ biofabrication line. The information technologies such as computer-aided design, related software and mathematical models and computer simulations are critically important integral technological components of organ printing technology which are enabling precision placement of tissue spheroids in 3D space according specially designed instructive "blueprint". Another technologies enabling organ printing include clinical cell sorters, scalable tissue spheroids biofabricators, microfluidics-based tissue spheroid encapsulators, robotic bioprinters, irrigation dripping perfusion bioreactors integrated with noninvasive and non-destructive biomonitoring systems and biosensors. This review outlines most important recent advances and potential future directions in the development of enabling technologies for organ printing.