Physical hydrogels prepared from natural biopolymers are the most popular components for bioinks. However, to improve the mechanical properties of the network, in particular its durability for long-lasting tissue engineering applications or its stiffness for bone/cartilage applications, covalent chemical hydrogels have to be considered. For that purpose, biorthogonal reactions are required to allow the inclusion of living cells within the bioink reservoir before the 3D printing procedure. Interestingly, such reactions also unlock the possibility to further multifunctionalize the network, adding bioactive moieties to tune the biological properties of the resulting printed biomaterial. Surprisingly, compared to the huge number of studies disclosing novel bioink compositions, no extensive efforts have been made by the scientific community to develop new chemical reactions meeting the requirements of both cell encapsulation, chemical orthogonality and versatile enough to be applied to a wide range of molecular components, including fragile biomolecules. That could be explained by the domination of acrylate photocrosslinking in the bioprinting field. On the other hand, proceeding chemoselectively and allowing the polymerization of any type of silylated molecules, the sol-gel inorganic polymerization was used as a crosslinking reaction to prepare hydrogels. Recent development of this strategy includes the optimization of biocompatible catalytic conditions and the silylation of highly attractive biomolecules such as amino acids, bioactive peptides, proteins and oligosaccharides. When one combines the simplicity and the versatility of the process, with the ease of functionalization of any type of relevant silylated molecules that can be combined in an infinite manner, it was obvious that a family of bioinks could emerge quickly. This review presents the sol-gel process in biocompatible conditions and the various classes of relevant silylated molecules that can be used as bioink components. The preparation of hydrogels and the kinetic considerations of the sol-gel chemistry which at least allowed cell encapsulation and extrusion-based bioprinting are discussed.