Wide-spectral saturable absorption (SA) in low-dimensional (LD) nanomaterials such as zero-, one-, and two-dimensional materials has been proven experimentally with outstanding results, including low saturation intensity, deep modulation depth, and fast carrier recovery time. LD nanomaterials can therefore be used as SAs for mode-locking or Q-switching to generate ultrafast fiber laser pulses with a high repetition rate and short duration in the visible, near-infrared, and mid-infrared wavelength regions. Here, we review the recent development of emerging LD nanomaterials as SAs for ultrafast mode-locked fiber laser applications in different dispersion regimes such as anomalous and normal dispersion regimes of the laser cavity operating in the near-infrared region, especially at ~1550 nm. The preparation methods, nonlinear optical properties of LD SAs, and various integration schemes for incorporating LD SAs into fiber laser systems are introduced. In addition to these, externally (electrically or optically) controlled pulsed fiber laser behavior and other characteristics of various LD SAs are summarized. Finally, the perspectives and challenges facing LD SA-based mode-locked ultrafast fiber lasers are highlighted.