The 3-5 μm mid-infrared band contains the atmospheric transmission window and the molecular fingerprint area, and has important research significance and development prospects in the fields of remote sensing, national defense, biomedicine and materials processing. Fiber lasers have good beam quality, high light-to-light conversion efficiency, good heat dissipation characteristics, compact structure and high reliability. The output wavelength of fiber lasers is currently expanding to the mid-infrared band, however, the phonon energy of the glass matrix is an important factor affecting the generation of mid-infrared lasers. The lower the phonon energy of the matrix material, the lower the multi-phonon relaxation rate of the rare-earth ions, thus promoting the radiation transition process. Heavy metal fluoride glasses demonstrate great potential for applications in mid-infrared fiber lasers due to their relatively low phonon energy, wide mid-infrared transmission window, high solubility of rare earth ions and high thresholds of laser damage resistance. With the increasing demand for 3-5 μm laser sources in the mid-infrared band, the development of a relatively low phonon energy fluoride glass is essential. The most extensively investigated fluoride fibers are fluorozirconate fibers such as ZBLAN fibers. In recent years, it has attracted interest as researchers have found that fluoroindate glasses have lower phonon energy, superior physical and chemical stability compared to fluorozirconate glasses. The relatively wide mid-infrared transmission window and low theoretical loss of fluoroindate fibers indicate that fluoroindate fibers have important research significance in the field of mid-infrared fiber lasers.This paper first introduces the research progress of fluoroindate glasses, including the investigation of the components, structure and luminescence properties of fluoroindate glasses. It is shown that the design of fluoroindate glass components is very complex and requires comprehensive consideration of the properties of each cation and application requirements. The structure of fluoroindate glasses is analyzed to be mainly composed of [InF₆]^3- octahedra. It is introduced the main rare earth ions that can achieve 3-5 μm mid-infrared fluorescence in fluoroindate glasses are Er³⁺ ions, Dy³⁺ ions, Ho³⁺ ions and Pr³⁺ ions, indicating that fluoroindate glasses are the promising gain material to achieve mid-infrared fiber lasers. Subsequently, the preparation of low-loss fluoroindate fibers is presented, laying the foundation for the establishment of mid-infrared fluoroindate fiber lasers. The research advances in fluoroindate fiber lasers are presented. The rare earth ions that can achieve 3-5 μm mid-infrared lasers in fluoroindate fibers are Er³⁺ ions, Dy³⁺ ions and Ho³⁺ ions, in which the ~3.9 μm laser of Ho³⁺ ions is the longest wavelength laser achievable in fluoride fibers, and the ~3.9 μm laser has been achieved only in fluoroindate fibers at room temperature so far, indicating that fluoroindate fibers are the potential mid-infrared fiber lasers. This paper reviews the latest research advances in the components and structures of fluoroindate glasses, presents the research advances of the luminescence properties of fluoroindate glasses. The preparation of low-loss fluoroindate fibers is presented, laying the foundation for the establishment of mid-infrared fluoroindate fiber lasers. The research advances of fluoroindate fiber lasers is reviewed, showing that fluoroindate fibers are the most promising material to achieve mid-infrared fiber laser. The preparation of low loss double cladding fluoroindate fibers can be achieved in the future by investigating the double cladding fluoroindate glass components and the double cladding fiber drawing process, which is conducive to achieving high power mid-infrared laser output. The output performance of the mid-infrared fiber laser can be further optimized by adjusting the rare-earth ion doping concentration of the fluoroindate fiber and constructing an all-fiber laser system to reduce the influence of the environment on the fiber laser system, thus achieving high power and high efficiency mid-infrared laser output.