An elementary reconsideration of first principles in aperture-domain processing of wave phenomena for reception (and, by reciprocity, for transmission) can yield revealing, and in some cases novel, insights into what can or cannot be achieved. The subjects covered here include direction-selective reception, superdirectivity, direction finding, focused near-field reception, circular arrays and circular modes in such arrays, and the new concepts of arrays composed of ‘random symmetrical pairs’, and of real gain in omnidirectional receiving antennas. The ideas are basic to all wave directional analysis and imaging applications, be they electromagnetic or acoustic, in radar or sonar, communications, navigation, surveillance or medical imaging.