A 2 μm tunable narrow-linewidth fiber laser has valuable applications in fields such as atmospheric detection, LiDAR, and medical detection. First, four common wavelength-tuning techniques are introduced, including diffraction grating filter tuning, volume Bragg grating filter tuning, acousto-optic filter tuning, and fiber Fabry-Perot filter tuning. Then, the advantages and disadvantages of these techniques are compared and analyzed. Next, we demonstrate three structures of narrow-linewidth lasers: linear cavity, ring cavity, and compound cavity, and compare their advantages and disadvantages. Subsequently, the current research results and technical challenges of narrow-linewidth, high power, and tunable fiber lasers in the 2 μm waveband are introduced. Finally, the technical development trends of tunable narrow-linewidth fiber lasers in the 2 μm waveband are prospected.