The incorporation of the material-based saturable absorber (SA) to generate mode-locked fiber laser (MLFL) has been extensively explored and demonstrated. However, the material-based SAs have some challenges in terms of optical damage threshold, design complexity, robustness, and stability due to several factors. Presently, several works have been demonstrated to address material-based SA fabrication issues. Therefore, this paper aims to comprehensively review the pros and cons of material-based SA in terms of material synthesis techniques, material characteristics, material-polymer composite, SA structure, and deposition techniques, along with current issues and challenges, and conclude with concrete recommendations. All the highlighted insights of this review will contribute to the increased efforts toward the development of the material-based SAs for the MLFL.