Alginates are polysaccharides that are produced naturally and can be isolated from brown sea algae and bacteria. Sodium alginate (SA) is utilized extensively in the field of biological soft tissue repair and regeneration owing to its low cost, high biological compatibility, and quick and moderate crosslinking. In addition to their high printability, SA hydrogels have found growing popularity in tissue engineering, particularly due to the advent of 3D bioprinting. There is a developing curiosity in tissue engineering with SA-based composite hydrogels and their potential for further improvement in terms of material modification, the molding process, and their application. This has resulted in numerous productive outcomes. The use of 3D scaffolds for growing cells and tissues in tissue engineering and 3D cell culture is an innovative technique for developing in vitro culture models that mimic the in vivo environment. Especially compared to in vivo models, in vitro models were more ethical and cost-effective, and they stimulate tissue growth. This article discusses the use of sodium alginate (SA) in tissue engineering, focusing on SA modification techniques and providing a comparative examination of the properties of several SA-based hydrogels. This review also covers hydrogel preparation techniques, and a catalogue of patents covering different hydrogel formulations is also discussed. Finally, SA-based hydrogel applications and future research areas concerning SA-based hydrogels in tissue engineering were examined.