For the treatment of patients with organs damaged or removed by medical indications, transplantation from donors is currently used. High risks of death, lifelong immunosuppression and an acute shortage of donor organs worsen the prospect of their use. Recent advances in the field of biofabrication indicate the imminent possibility of the emergence of real alternatives to the methods currently used. The biomaterials used create a three-dimensional space in which cells can attach, grow and form new tissues with an appropriate structure and function. Modern research pays special attention to the choice of materials and technologies to ensure the mechanical and physiological properties of the newly created tissue. The review examines modern technologies of regenerative medicine, as well as the results of experimental studies in the field of biofabrication for creating scaffolds, tissue-engineering structures, as well as hollow and fragments of complex organs that already have practical implementation. © 2019 Russian Transplant Society. All rights reserved.