A wide variety of hydrogels have been proposed for tissue engineering applications, cell encapsulation, and bioinks for bioprinting applications. Cell-laden hydrogel constructs rely on natural hydrogels such as alginate, agarose, chitosan, collagen, gelatin, fibroin, and hyaluronic acid (HA), as well as on synthetic hydrogels such as poloxamers (Pluronics®) and polyethylene glycol (PEG). Alginate has become more and more important in the last years, thanks to the possibility to prepare alginate hydrogels suitable for cell encapsulation mainly because of the mild and reversible cross-linking conditions. In this paper alginate will be described in detail with respect to its chemistry, cross-linking behavior, biocompatibility, manufacturing capacity, and possible modifications.