12.1 Introduction This chapter briefly reviews the important theoretical aspects of eigenimage processing and demonstrates the unique properties of this approach using various examples such as the separation of up and downgoing waves, multiple attenuation, and residual static correction. In particular, we will compare the eigenimage technique to the well-known frequency-wave number f-k, method, (Treitel et al., 1967), and discuss important differences which arise especially with respect to spacial aliasing and the separation of signal and noise.