In this paper, we present a general theory of aperiodic subwavelength arrays for controlling electromagnetic waves. The considered platform is formed by an array of electrically small loaded scatterers above a ground plane. While the array is geometrically periodic and fixed, all the loads can be in general different, so that the distributions of currents induced by plane waves are not periodic. To allow analytical solutions, we study arrays of thin wires or strips loaded by bulk loads. We demonstrate a way of creating tunable and reconfigurable multifunctional devices, on examples of superdirective beam splitters, focusing metalenses, and absorbers going beyond perfect absorption. Contrary to the constraints imposed by the Floquet theorem in periodic counterparts like periodic metasurfaces or metagratings, where a fixed angle of incidence and period dictate the propagating directions of reflected waves, the proposed aperiodic designs allow controlling all propagating modes in any direction, which provides more freedom in manipulating electromagnetic waves. We hope that these results can be useful in multiple applications, such as telecommunications, radar techniques, signal processing, and energy harnessing.