In general, the mainstream conventional signal processing of current sonar and ultra-sound systems consists of a selection of temporal and spatial processing algorithms [2–6]. These algorithms are designed to increase the signal-to-noise ratio (SNR) for improved signal delectability while simultaneously providing parameter estimates such as frequency, time-delay, Doppler and bearing for incorporation into localization, classification and signal tracking algorithms. Their implementation in real time systems had been directed at providing high-quality, artifact-free conventional beamformers, currently used in operational ultrasound and sonar systems. Thus, space-time processing is the fundamental processing concept in sonar and ultrasound systems. The chapter outlines the context in which the sonar or the ultrasound problem can be viewed in terms of simple models of acoustic signals and noise fields.