Alginate is a natural polysaccharide that typically originates from various species of algae. Due to its low cost, good biocompatibility, and rapid ionic gelation, the alginate hydrogel has become a good option of bioink source for 3D bioprinting. However, the lack of cell adhesive moieties, erratic biodegradability, and poor printability are the critical limitations of alginate hydrogel bioink. This review discusses the pivotal properties of alginate hydrogel as a bioink for 3D bioprinting technologies. Afterward, a variety of advanced material formulations and biofabrication strategies that have recently been developed to overcome the drawbacks of alginate hydrogel bioink will be focused on. In addition, the applications of these advanced solutions for 3D bioprinting of tissue/organ mimicries such as regenerative implants and in vitro tissue models using alginate-based bioink will be systematically summarized.