Due to the manifestation of fascinating physical phenomena and materials science, two-dimensional (2D) materials have recently attracted enormous research interest with respect to the fields of electronics and optoelectronics. There have been in-depth investigations of the nonlinear properties with respect to saturable absorption, and many 2D materials show potential application in optical switches for passive pulsed lasers. However, the Eigen band-gap determines the responding wavelength band and constrains the applications. In this paper, based on band-gap engineering, some different types of 2D broadband saturable absorbers are reviewed in detail, including molybdenum disulfide (MoS₂), vanadium dioxide (VO₂), graphene, and the Bi₂Se₃ topological insulator. The results suggest that the band-gap modification should play important roles in 2D broadband saturable materials and can provide some inspiration for the exploration and design of 2D nanodevices.