Tunable single-frequency fiber lasers (TSFFLs) possess the characteristics of wide tuning range, high optical signal-to-noise ratio (OSNR), narrow linewidth, low noise, and excellent compatibility. They also have attracted extensive attention from researchers at home and abroad because of their important application value in the spectroscopy, optical detection, optical sensing, fiber communication and so on. In this paper, the tuning and longitudinal-mode selection key techniques of TSFFLs were introduced briefly. The TSFFLs with different wavelengths of 1.0 μm, 1.5 μm, 2.0 μm, and mid-infrared were summarized and their research status at home and abroad was reviewed. The results obtained in tuning range, laser linewidth, OSNR, power scaling, flatness of output power, and other output performances were also shown. In addition, combined with our new progress, the recent development of TSFFLs based on compound cavity structure was introduced. Furthermore, the future development trend of TSFFLs was also forecasted.