Regenerative medicine is being revolutionized by the combination of cellular therapies and 3D bioprinting, which permits the precise creation of intricate, particular tissue for each patient constructs for tissue repair and organ replacement. Cell-laden bioinks can be precisely deposited using methods like inkjet and extrusion-based bioprinting (EBB), which promotes functional tissue-like constructs with excellent cell viability and spatial fidelity. Because of their biocompatibility and gelation ability, hydrogel-based bioinks—especially those made from sodium alginate (SA)—are frequently utilized. However, physical and chemical modifications are required due to SA's intrinsic mechanical instability, rapid degradation, and lack of bioactivity. Chemical techniques that improve mechanical strength, biodegradability, and biological interactions include oxidation, esterification, sulfation, amidation, methacrylation, and polymer grafting. Physical techniques that can enhance rheology, printability, structural integrity, and cell adhesion include blending with natural or synthetic polymers such as PEGDA, chitosan, pectin, CMC, & carbopol introducing nanomaterials. In multi-head bioprinting, polycaprolactone works as a structurally stable synthetic framework; hydrophobicity and bioinertness can be controlled by surface treatments and polymer blending. Ionic crosslinking using the "egg-box" paradigm stabilizes the structure of hydrogels made of alginate. The suitability of bioink for extrusion printing is confirmed by characterization methods such as FTIR, XRD, DSC, SEM, and thorough rheological evaluations. MTT experiments for in vitro cytocompatibility show >70% cell viability in all formulations. The development of stable, biologically active & adjustable tissue constructions is made possible by advancements in chemical and physical modification techniques, enhanced bioink formulations, and bioprinting methods. These improvements have the potential to significantly accelerate the clinical application of biofabrication for tissue restorationfacilitating medication delivery and effective tissue regeneration