Abstract: High-power narrow-linewidth fiber lasers based on single-stage amplifier structure have the advantages of simple structure, high reliability, and low cost, and have found applications in nonlinear frequency conversion, gravitational wave detection, and coherent beam combining. Due to temporal instability caused by self-pulsing in multi-longitudinal-mode oscillating seeds, such lasers can generate severe stimulated Raman scattering and spectral broadening during power amplification and reduce spectral purity. This paper introduces the limiting factors affecting high-power narrow-linewidth fiber lasers with single-stage amplifier structure, and focuses on the generation mechanism of self-pulsing effects including sustained self-pulsing and self-mode-locking pulses in multi-longitudinal-mode oscillating seeds. The optimization measures and underlying theories for both seed sources and amplifiers are reviewed in detail. For seed sources, methods such as increasing the intracavity photon lifetime, composite cavities based on the Vernier effect, spectral shaping of output-coupler fiber Bragg gratings, and external-feedback/long-passive-fiber configurations are discussed; for amplifiers, the suppression of SRS, self-phase modulation, and transverse mode instability is addressed, covering pump-configuration optimization, large-mode-area and novel gain fibers, and chirped and tilted fiber Bragg gratings. Representative progress in recent years is surveyed, including single-stage narrow-linewidth fiber lasers delivering 2.4-6 kW output power with near-diffraction-limited beam quality, SRS suppression ratios beyond 30 dB, and record spectral brightness. Finally, the development trends are analyzed, with emphasis on balancing nonlinear-effect suppression against transverse-mode-instability mitigation, systematic optimization of composite-cavity parameters, adoption of novel fibers and integrated devices, and the move toward compact oscillator–amplifier integrated architectures.