The progress in the field of tissue engineering is largely driven by the development of 3D laser printing technology, which makes it possible to create hydrogel scaffolds containing cells (the so-called tissue engineering constructs), in the course of photoinduced radical reactions of polymerization and crosslinking. The review considers the main mechanisms and features of such reactions, presents the most common materials for photocompositions in the form of natural and synthetic polymers and precursors, describes the activation mechanism for various types of photoinitiators. Advances in the field of photopolymerization enable the application of modern laser 3D printing techniques based on extrusion and stereolithography to design tissue constructions in a wide range of sizes, various shapes with a finely organized architecture, containing cells without losing their functional activity. The integration of such methods with the methods of bioengineering and cell technology is discussed, including for the creation of tissue-specific and in vivo polymerized constructs.