Technologies of 3D- and 4D-bioprinting make it possible to restore or replace tissues and organs, solving the problem of the lack of donor resources and reducing the risks of implant rejection. This article presents the results of a two-stage global survey of specialists in tissue engineering on the prospects of bioprinting in preclinical studies and clinical practice. A picture of possible tracks and horizons upon which the implementation of the considered solutions is possible is presented. According to the results of the survey, in the next two decades it will be possible to recreate tissues and organs suitable for implantation and drug testing. There will be a market for bioprinted products, the problem of organ shortages and adverse reactions to drugs will be solved. These changes may significantly affect not only the practice of biomedical research, drug testing, and medicine, but also the healthcare sector in general, which implies the need for a preventive review of current policies. A practical and accessible tool for identifying and interviewing a large number of experts around the world is proposed, which may be useful for new Foresight studies.