Three-dimensional bioprinting is a powerful technique for manufacturing improved engineered tissues. Three-dimensional bioprinted hydrogels have significantly advanced the medical field to repair cartilage tissue, allowing for such constructs to be loaded with different components, such as cells, nanoparticles, and/or drugs. Cartilage, as an avascular tissue, presents extreme difficulty in self-repair when it has been damaged. In this way, hydrogels with optimal chemical and physical properties have been researched to respond to external stimuli and release various bioactive agents to further promote a desired tissue response. For instance, methacryloyl gelatin (GelMA) is a type of modified hydrogel that allows for the encapsulation of cells, as well as oxygen-releasing nanoparticles that, in the presence of an aqueous medium and through controlled porosity and swelling, allow for internal and external environmental exchanges. This review explores the 3D bioprinting of hydrogels, with a particular focus on GelMA hydrogels, to repair cartilage tissue. Recent advances and future perspectives are described.