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• Reviews the feasibility of mono-elemental materials for saturable absorber. • Reviews the synthesis method and material characterization of mono-elemental materials. • Reviews the fabrication of saturable absorber and its nonlinear optical characteristics. • Reviews the integration of saturable absorber for near-infrared mode-locked fiber laser. • Discusses the issues and challenges of mono-elemental saturable absorber in near-infrared mode-locked fiber laser. Two-dimensional mono-elemental material is an excellent saturable absorber candidate with low saturation intensity, large modulation depth, high nonlinearities, and fast recovery time of excited carriers. Typically, these mono-elemental material with two-dimensional structure possesses tunable bandgap from metallic to semiconducting according to different number of layers. The integration of these materials as the saturable absorber has exploited the development of near-infrared mode-locked fiber lasers. Therefore, this review is intended to provide an up-to-date information to the development of mono-elemental saturable absorber for the advances in near-infrared mode-locked fiber laser, with emphasis on their material properties, synthesis process and material characterization. Meanwhile, issues and challenges of the review research topic will be highlighted and addressed with recommendations. [ABSTRACT FROM AUTHOR]