Hyperspectral images are the only type of images where we can verbalize about spectral resolution. The spectral resolution is defined as the interval or disseverment between different wavelengths quantified in a concrete wavelength range. Conspicuously, the more spectral channels acquired in a more diminutive wavelength range, the higher the spectral resolution will be in the scenario. Moreover, when a hyperspectral image is acquired, it is stored in a file where the spectra must be injuctively authorized in a logical manner in order to be able to reconstruct the data cube in any software. To store the file in the board or any device, have to use an algothirm to compress it in proper way to retrieve it again without any loss. In this paper, going to see and discuss about the various algorithms and techniques used to compress the hyperspectral images proposed by experts in this field, which may helpful for the future scholars in this area to see a glance around compression techniques applied on hyperspectral images for better performance of the captured data.