Optical information processing can perform a myriad of signal processing operations. It is primarily due to the complex amplitude processing capability. Optical information processors are capable of performing one- or two-dimensional operations using simple linear operators. However, it would not happen without the support of coherent property of illumination. We discuss the coherent optical complex transformation, by which information data processing can be exploited. A brief scan of Fourier and spatial domain processing, composite filtering, larger capacity photorefractive processing, optical neural computing, and others is shown.