In the mid-infrared band, 3-5 μm is a very special window, and it covers many intrinsic absorption peaks of molecules and atoms. Moreover, it is one of the transparent windows of the atmosphere. Therefore, lasers working in this band have great application prospects in various fields such as gas detection, material processing, biomedicine, military confrontation and remote sensing. Compared with quantum cascade lasers, solid-state lasers, and optical parametric lasers, fiber lasers have advantages of excellent beam quality, good heat dissipation, easy miniaturization and integration, high conversion efficiency, and good robustness. It stands out in the field of mid-infrared laser and has become a cutting-edge research hotspot in the field of laser. At present, the methods of generating 3-5 μm mid-infrared fiber laser can be roughly divided into the following three categories: 1) Direct lasing method based on rare earth ion-doped fiber; 2) Nonlinear wavelength frequency shift; 3) Supercontinuum generation. However, the latter two schemes usually using rare earth doped fiber lasers as the pump sources. In addition, the rare earth ion doped fiber lasers have advantages of high gain, large bandwidth, high nonlinear, easy integration and so on, and have gradually become one of the ideal platforms for mid-infrared. Therefore, the rare earth ion doped fiber lasers are the foundation and core of the development of 3-5 μm band laser technology.Three kinds of gain ions, Er³⁺, Ho³⁺ and Dy³⁺, which are commonly used in 3-5 μm fiber lasers, are introduced in detail. The current development of continuous and pulsed fluoride fiber lasers based on these ions doping is reviewed, respectively. In recent years, the performance of 3-5 μm continuous wave fiber lasers has been greatly improved. The output power of 15 W, 10.1 W and 200 mW was achieved in the 3.5 μm (Er³⁺: ZBLAN), 3.2 μm (Dy³⁺: ZBLAN), and 3.9 μm (Ho³⁺: InF₃), respectively. Moreover, broadly tuning of ~700 nm is realized in the spectral range of 2.710-3.415 µm for a Dy³⁺: ZBLAN continuous wave laser. On the other hand, with the rapid development of mid-infrared gain-switching, Q-switching technology and related devices, 3-5 μm short-pulse lasers have made great technical breakthroughs. The largest output power of 1.4 W is achieved in a 3.22 μm Er³⁺: ZBLAN fiber. However, there is still a long way to go for further improvement in stability, peak power and pulse energy. Ultra-short pulse fiber lasers with 3-5 μm band have achieved breakthroughs, the longest wavelength of 3.61 μm is achieved for mode-locked mid-infrared pulses. But the mode-locking pulse performance, including pulse width compression, power/energy improvement, wavelength expansion, noise suppression and stability improvement, still have many problems to be solved and studied. In recent years, with the development and maturity of fluoride fiber drawing and doping techniques and the optimization and innovation of pumping mode, significant progress has been made in the field of middle infrared fiber lasers based on rare earth ions doping. The reported rare earth doped mid-infrared fiber lasers in the 3-5 μm band are reviewed from the perspective of continuous lasers and pulse lasers, respectively. The following trends are summarized: (1) The output power will be further improved. In recent years, continuous fiber lasers over 3 μm have achieved output power of 15 W. However, compared with the ~2.8 μm fiber lasers, the output power of this band still has a large room for improvement. In future studies, the output power can be further increased to tens or even hundreds of watts by further optimizing the pump structure, optimizing the preparation process of fluoride fiber, optimizing the fiber welding technology and the performance of fiber passive devices such as fiber grating and fiber end caps. (2) The wavelength will be further extended to longer wavelengths. For rare-earth ions doped continuous laser, the current recorded wavelength output is 3.92 μm, and no further breakthrough has been achieved since 2018, and the field of rare-earth ion doped fiber laser >4 μm is still a blank. In future studies, it is worthwhile to further extend the output wavelength by developing new doping ions such as Tb ³⁺. (3) Toward all-fiber configuration. There is no doubt that the all-fiber system is in line with the development trend of fiber lasers. In the band of 3-5 μm, due to the lack of fiber functional devices and the imperfection of high quality fiber processing technology, the overall all-optical fiber level is low. In the future research, the development of active and passive fiber functional devices for mid-infrared laser generation should be accelerated. It can be predicted that in the near future, high performance, all-fiber 3-5 μm rare earth ion-doped mid-infrared laser will move from the laboratory to many practical fields, and promote the technical development and progress of industry, medical, national defense and other related fields.