Many state-of-the-art wireless systems, such as long distance mesh networks and high bandwidth networks using mm-wave frequencies, require high gain antennas to overcome adverse channel conditions. These networks could be greatly aided by adaptive beamforming antenna arrays, which can significantly simplify the installation and maintenance costs (e.g., by enabling automatic beam alignment). However, building large, low cost beamforming arrays is very complicated. In this paper, we examine the main challenges presented by large arrays, starting from electromagnetic and antenna design and proceeding to the signal processing and algorithms domain. We propose 3-dimensional antenna structures and hybrid RF/digital radio architectures that can significantly reduce the complexity and improve the power efficiency of adaptive array systems. We also present signal processing techniques based on adaptive filtering methods that enhance the robustness of these architectures. Finally, we present computationally efficient vector quantization techniques that significantly improve the interference cancellation capabilities of analog beamforming architectures.