In this thesis, efficient methods are presented to calibrate large or small aperture array systems containing different types of uncertainties. specifically the challenge of reducing the number of external sources required to calibrate an array is addressed and array calibration methods suitable for use when sources may be operating in the "near-far" field of the array are developed. Together, this can ease the overheads involved in calibrating and recalibrating an array system. In addition to presenting novel array calibration algorithms, this thesis also presents a novel transformation allowing a planar array to be expressed as a virtual uniform linear array of a much larger number of elements. This allows the array manifold of a planar array, which in general consists of non-hyperhelical curves, to be expressed using a number of hyperhelices which each correspond to the array manifold of a linear array. This hyperhelical structure has the potential to ease calibration overheads as well as having many other potential applications in array processing. This thesis presents novel pilot and auto array calibration schemes for estimating different types of array uncertainties. A novel pilot calibration algorithm is proposed whereby a single source transmitting from a known location (i.e. a pilot) at two carrier frequencies is used to estimate geometrical uncertainties in a planar array. This is achieved by exploiting the frequency dependence on the boundary between the "near-far" and "far" field of the array. In addition, an auto-calibration method is presented which doesn't require any external sources to estimate array uncertainties. Here, geometrical, complex gain and local oscillator (i.e. frequency and phase) uncertainties associated with the array elements are considered. In this approach, array elements transmit in turn to the others which operate as an array receiver. Large and small array apertures are investigated. Throughout the thesis, extensive computer simulations are presented to analyse the performance of the algorithms developed.