Abstract: Compressed sensing is a new sampling theory, which captures and encodes signals at a rate significantly below Nyquist rate provided that these signals are sparse or compressible. This paper reviews the theoretical framework of compressed sensing. It first employs non-adaptive linear projections to preserve the structure of the signal, and then the signal recovery is conducted accurately or in all probability by using an optimal reconstructed algorithm from these projections. Its related applications in optical imaging systems are introduced, such as single-pixel camera, super thin imagers, coded aperture imagers, multiplexing intelligent imagers, spectral imagers, and CMOS imagers. Some prospects and suggestions about further works on this theory are also presented.