Three-dimensional (3D) bioprinting is a promising and innovative biomanufacturing technology, which can achieve precise position controlling of cells and extracellular matrix components, and further create complex and functional multi-cellular tissues or organs in a 3D environment. Bioink in the form of the cell-loaded hydrogel is most commonly used in bioprinting, and it is vital to the process of bioprinting. The bionic scaffold should possess suitable mechanical strength, biocompatibility, cell proliferation, survival, and other biological characteristics. The disadvantages of natural polymer hydrogel materials include poor mechanical properties as well as low printing performance and shape fidelity. Over the past years, a series of synthetic, modified, and nanocomposite hydrogels have been developed, which can interact through physical interactions, chemical covalent bond crosslinking, and bioconjugation reactions to change the characteristics to satisfy the requirements. In this review, a comprehensive summary is provided on recent research regarding the unique properties of hydrogel bioinks for bioprinting, with optimized methods and technologies highlighted, which have both high-value research significance and potential clinical applications. A critical analysis of the strengths and weaknesses of each hydrogel-based biomaterial ink is presented at the beginning or end of each section, alongside the latest improvement strategies employed by current researchers to address their respective shortcomings. Furthermore, we propose potential repair sites for each hydrogel-based ink based on their distinctive repair features, while reflecting on current research limitations. Finally, we synthesize and analyze expert opinions on the future of these hydrogel-based bioinks in the broader context of tissue engineering and regenerative medicine, offering valuable insights for future investigations.