Methacrylic anhydride-based hydrogels, derived by introducing methacryloyl groups to various polymer side chains, are promising bioinks for 3D printing in medical applications. These hydrogels combine the inherent biocompatibility and therapeutic benefits of their parent polymers with the unique photocrosslinking properties conferred by the methacryloyl groups, allowing the precise control over their mechanical properties through light-curing parameters. Using three-dimensional (3D) biological compression, these hydrogels serve as bioinks for producing scaffolds with optimal porosity, facilitating cell adhesion, proliferation, and differentiation. This technology enables the precise spatial distribution of bioactive substances, offering targeted therapeutic treatment and controlled release. This review delved into recent advancements in bioprinting technologies, outlined the preparation of methacrylic anhydride-based bioinks, and summarized factors influencing the resulting biological and mechanical properties of bioscaffolds. Additionally, the properties and applications of methylpropionic anhydride-based hydrogels in various medical fields were discussed, addressing current limitations and future challenges in integrating these hydrogels with 3D bioprinting for clinical applications.