Abstract: Hyperspectral remote sensing has already become the advanced science and technology in the field of remote sensing, which plays an important function on military scout and national economy. The number of spectral channels can reach in the hundreds, with the increase of spectral resolution, the datasets of hyperspectral imagery become larger and larger. For the hyperspectral imagery acquired by imaging spectrum instrument on satellite the huge datasets have brought great press for data storage and transmission, which restricts the practical applications of hyperspectral imagery, therefore, it is necessary to compress hyperspectral imagery by efficient compression technique. The compression technique for hyperspectral imagery can lossy compression and lossless compression, For practical application, the compression type should be selected according to the application requirement. In this paper, the basic concept of hyperspectral remote sensing technique is introduced firstly, then, the research progress of hyperspectral imagery compression technique is summarized, which includes lossless compression and lossy compression. Finally, the research direction for hyperspectral imagery compression is pointed out.