Abstract: Hydrous minerals on the Martian surface are closely related to early aqueous activity. Analyzing their spatial distribution and abundance variations is essential for understanding the early aqueous environment and geological evolution of Mars, which can provide important insights into Martian habitability evolution and extraterrestrial life exploration. As one of the key techniques for studying Martian hydrous minerals, hyperspectral remote sensing can collect abundant spatial and spectral information from the Martian surface, which provides important data support for classification and quantitative retrieval. Compared with Observatoire pour la Minéralogie, l'Eau, les Glaces, et l'Activité (OMEGA) and Mars Mineralogical Spectrometer (MMS) data, the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) provides higher spatial and spectral resolutions and covers the visible to near-infrared wavelength range, making it the most widely used hyperspectral dataset for Martian surface studies. In recent years, significant advances have been achieved in the detection of hydrous minerals, mineralogical composition analysis, and abundance inversion using CRISM data, providing valuable insights into the paleoclimatic environment of Mars and the history of its aqueous activities. However, due to the inherent complexity of Martian hyperspectral data, together with the scattered spatial distribution and low abundance of hydrous minerals, Mars hyperspectral remote sensing processing and interpretation still face significant challenges. With the rapid development of artificial intelligence, current research is shifting from traditional spectral parameter method toward more intelligent and automated approaches, and entering a new stage of development. This paper systematically reviews recent advances in hyperspectral image processing of Mars based on CRISM data, with a particular focus on the development of hyperspectral image denoising, mineral classification and identification, and quantitative abundance inversion. In terms of mineral classification and identification, the development of spectral parameter methods, spectral matching and similarity measurement methods, target detection methods, traditional machine learning approaches, and deep learning approaches is systematically reviewed. For quantitative mineral abundance inversion, emphasis is placed on linear spectral unmixing models, nonlinear spectral mixing models, and neural network-based abundance inversion methods. Furthermore, the key scientific problems addressed by these approaches, together with their technical characteristics, advantages, and limitations, are comprehensively summarized. In addition, the major challenges faced by current studies, including insufficient training samples, mixed-pixel effects, limited model generalization capability, and inadequate geological interpretability, are analyzed in depth, and potential solutions are discussed. Based on these analyses, future research directions are proposed to provide references for the accurate and efficient identification of hydrous minerals on Mars as well as high-precision mineral abundance inversion.