Mid-infrared optical fiber is an important tool in the field of mid-infrared optics with applications in mid-infrared laser generation and transmission, biomedical detection, environmental detection and other fields. However, traditional mid-infrared optical fibers suffer from fabrication difficulties and poor chemical stability of substrate materials, substantially limiting their developments. Compared with solid-core fibers, hollow-core fibers release the dependence on the substrate materials. By constructing microstructures in the cladding, light is confined, in the central air core, thus providing an ideal transmission channel with low loss, low dispersion, low delay, low nonlinearity, and high damage threshold. It opens a new path in the development of mid-infrared fibers.This paper reviews the development history, research status and application prospects of silica-based and soft glass-based mid-infrared hollow-core fibers in terms of fiber structure, fabrication method, material absorption and transmission performance. By numerical simulations, we show the relationship between absorption loss and confinement loss with core size, wall thickness and wavelength in silica-based single-ring structure and nested tube structure anti-resonant hollow-core fiber. It provides design guidelines for the low-loss mid-infrared anti-resonant hollow-core fiber.Compared with mid-infrared (MIR) solid core fiber, MIR hollow-core fibers (HCF) have overcome the material absorption of silica in the mid-infrared band, expanded the guiding window of silica-based HCF, and realized low loss light transmission in the mid-infrared band. The characteristics of low dispersion, low delay, low nonlinearity and high damage threshold make more advantageous in the field of mid-infrared laser. Although the bending loss of MIR-HCF is continuously reduced by iteration and optimization of the fiber structure, there is still a certain gap between them and solid core fiber, which will be an important research direction in the field of mid-infrared hollow core fiber in the future. Currently, mid-infrared hollow fibers have a wide range of applications in the fields of mid-infrared laser generation and transmission, biomedical sensing, communication and other fields. In addition to silica materials, many soft glass materials (such as sulfide glass and tellurite glass) have inherent low material absorption properties, which provide more material choices for the preparation of MIR-HCF. In the future, the development of MIR-HCF will continue in improving the fabrication technology, optimizing the fiber structure, broadening the transmission window, reducing the attenuation and be applied to various fields.