Compression of hyperspectral images is an important topic for transmission and storage of data. There are several compression approaches proposed in the literature. Performance analysis of these methods is generally measured by image quality metrics. However, image quality metrics are not capable of determining compression performance for a specific application area. In this paper, popular compression approaches JPEG2000, PCA+JPEG2000, DWT+JPEG2000, 3D-SPECK, and 3D-TARP are evaluated in terms of unmixing, anomaly detection, target detection, and classification performances. Experimental evaluations are carried out on four hyperspectral datasets, and obtained results are interpreted.