Coded aperture snapshot spectral imager (CASSI) based on compressed sensing can capture a three-dimensional (3-D) data cube information in one snapshot without scanning, so it is a kind of novel spectral imaging technique with good prospects. In this paper, the data flow procession of two kind of CASSI were studied, which similarities and differences were depicted. The basic principle of the encoded representation of both spectral information and 2-D spatial information of a scene were presented. The numerical estimation techniques based on the compressive sensing theory were applied to reconstruct 3-D data cube.