Alginate, categorized as a natural-based biodegradable polymer, stands out for its inherently exclusive properties. Although this unique polymer is widely processed using film, coating, and membrane technologies for different usage areas, textile applications are still limited. This study aims to compile promising approaches that will pave the way for the use of wet-spun alginate filaments in textile applications. In this regard, this study provides information about the molecular structure of alginate, the gel formation mechanism, and cross-linking using different techniques. Our literature review categorizes parameters affecting the mechanical properties of wet-spun alginate filaments, such as the effect of ion source and spinning dope concentration, needle diameter, temperature, and coagulants. Following this, a detailed and comprehensive literature review of the various approaches, such as use of additives, preparation of blended filaments, and grafted nanocrystal addition, developed by researchers to produce composite alginate filaments is presented. Additionally, studies concerning the use of different cations in the coagulation phase are reported. Moreover, studies about the functionalism of wet-spun alginate filaments have been offered.