The purpose of this research is to employ non-uniform arrays in different active and passive sensing applications for both narrowband and wideband operations, while providing a multitude of array processing methodologies that assist in dealing with the different encountered challenges. The problem of direction-of-arrival (DOA) estimation using non-uniform arrays is considered. The different challenges that are treated include the reduction of the available degrees-of-freedom (DOFs), the presence of coherent targets, and the mutual coupling effect in practical antenna arrays. Multi-frequency operation is exploited to increase the DOFs that are available for DOA estimation using both high-resolution subspace and sparse reconstruction techniques. In addition, a sparsity-based interpolation technique is presented to perform DOA estimation with increased DOFs. Moreover, a DOA estimation approach for a mixture of coherent and uncorrelated targets based on sparse reconstruction and active non-uniform arrays under narrowband signal platform is proposed. The aforementioned approaches deal with ideal operational scenarios. To address a more practical scenario, various methods for DOA estimation using non-uniform arrays in the presence of mutual coupling are presented. Extensive numerical simulations which validate the different proposed methods are also included.