Hyperspectral imaging can detect targets that cannot be detected in broadband remote sensing, greatly improving the ability to describe and distinguish ground object categories. However, the increase in band dimensionality also brings many problems, such as insufficient samples, high dimensionality, and a large amount of redundant information, which poses a huge challenge to feature extraction in hyperspectral images. This article reviews hyperspectral image feature extraction algorithms from four aspects: dimensionality reduction, feature extraction, feature matching, and image synthesis. Elaborated on the advantages and disadvantages of various algorithms. This article reviews classification algorithms for remote sensing images from two aspects: feature space method and spectral matching method. Elaborated on the iteration and comparison of traditional algorithms and new technologies. At the same time, from the perspective of the drone industry, the difficulties faced by existing algorithms and the development trend of hyperspectral images were elaborated. It is particularly critical to select accurate methods based on actual data in specific applications.