Many imaging systems use arrays of individual elements to sense the propagating field produced by an object. Through signal processing techniques such as beamforming, an image of the object may then be formed. In addition to such passive arrays, imaging systems may use active arrays to both illuminate an object with a radiated field and to record the reflected field. Examples of imaging array systems occur in radio astronomy, sonar, microwave imaging and ultrasound imaging. This research is aimed at developing fundamental new results for array design and associated signal processing, based on recent developments on the characterization of array performance in linear imaging. Active imaging systems (e.g. ultrasound imaging arrays) are a particular focus of this investigation, although some of the proposed work also addresses passive arrays. Using the idea of the "coarray", this work will consider how to deploy array elements (and associated hardware) in the most efficient way to obtain large array apertures and high resolutions. The results will allow minimum redundancy active arrays and minimum complexity active arrays to be specified. This research on arrays includes a study of their characteristics under real operating conditions, under real operating conditions, and will extend to some experimental work with an acoustic array system.