3D bioprinting has gained visibility in regenerative medicine and tissue engineering due to its applicability. Over time, this technology has been optimized and adapted to ensure a better printability of bioinks and biomaterial inks, contributing to developing structures that mimic human anatomy. Therefore, cross-linked polymeric materials, such as hydrogels, have been highly targeted for the elaboration of bioinks, as they guarantee cell proliferation and adhesion. Thus, this short review offers a brief evolution of the 3D bioprinting technology and elucidates the main hydrogels used in the process.