In this dissertation, we examine and address the main challenges presented by large arrays, starting from electromagnetic/antenna and radio circuit design and proceeding to the signal processing and algorithms domain. We propose 3-dimensional antenna array structures that realize large gains and scan angles at a much reduced size and form factor compared with conventional planar antennas. At the circuit level, we propose a hybrid RF/digital beamforming radio architecture that takes advantage of low cost silicon integration to reduce the overall component count and power consumption levels of the system without limiting the capacity. We consider different techniques for implementing compact beamformers reliably at high radio frequencies, and present signal processing techniques based on adaptive filtering methods for optimizing those beamformers. The performance implications of low precision analog beamformers and implementation errors are also analyzed and quantified, and computationally efficient vector quantization techniques that take advantage of the size and scale of the arrays to compensate for low precision are proposed. We validate our approach with mathematical proofs and computer simulations.