Alginate is an excellent biodegradable and renewable material that is already used for a broad range of industrial applications, including advanced fields, such as biomedicine and bioengineering, due to its excellent biodegradable and biocompatible properties. This biopolymer can be produced from brown algae or a microorganism culture. This review presents the principles, chemical structures, gelation properties, chemical interactions, production, sterilization, purification, types, and alginate-based hydrogels developed so far. We present all of the advanced strategies used to remarkably enhance this biopolymer’s physicochemical and biological characteristics in various forms, such as injectable gels, fibers, films, hydrogels, and scaffolds. Thus, we present here all of the material engineering enhancement approaches achieved so far in this biopolymer in terms of mechanical reinforcement, thermal and electrical performance, wettability, water sorption and diffusion, antimicrobial activity, in vivo and in vitro biological behavior, including toxicity, cell adhesion, proliferation, and differentiation, immunological response, biodegradation, porosity, and its use as scaffolds for tissue engineering applications. These improvements to overcome the drawbacks of the alginate biopolymer could exponentially increase the significant number of alginate applications that go from the paper industry to the bioprinting of organs.