Snapshot compression imaging technology can obtain the three-dimensional spatial-spectral information from the target within a single exposure imaging, which has a significant advantage in the detection and identification for moving targets compared with the traditional scanning imaging method. With the development of information technology and computer processing performance, computational imaging has gradually become one of the most important technologies for solving optical imaging problems. By building a physical model of the imaging device and mathematically optimizing the back-end processing, which can break through the limitations of the imaging model and detector, the traditional two-dimensional imaging can be extended to more observation dimensions. In this paper, the current research status of snapshot hyperspectral imaging technology based on coding compression is summarized from three aspects: spatial coding, wavelength coding and phase coding. And we summarize and analyze the development trend of traditional methods and deep learning methods, as well as look forward to the development of snapshot hyperspectral imaging technology based on coding compression.