The objective of the dissertation research is to investigate noise reduction methods for binaural hearing aids based on array and statistical signal processing and inspired by a human auditory model. In digital hearing aids, wide dynamic range compression (WDRC) is the most successful technique to deal with monaural hearing losses. This WDRC processing is usually performed after a monaural noise reduction algorithm. When hearing losses are present in both ears, i.e., a binaural hearing loss, independent monaural hearing aids have been shown not to be comfortable for most users, preferring a processing that involves synchronization between both hearing devices. In addition, psycho-acoustical studies have identified that under hostile environments, e.g., babble noise at very low SNR conditions, users prefer to use linear amplification rather than WDRC. In this sense, the noise reduction algorithm becomes an important component of a digital hearing aid to provide improvement in speech intelligibility and user comfort. Including a wireless link between both hearing aids offers new ways to implement more efficient methods to reduce the background noise and coordinate processing for the two ears. This approach, called binaural hearing aid, has been recently introduced in some commercial products but using very simple processing strategies. This research analyzes the existing binaural noise-reduction techniques, proposes novel perceptually-inspired methods based on blind source separation (BSS) and multichannel Wiener filter (MWF), and identifies different strategies for the real-time implementation of these methods. The proposed methods perform efficient spatial filtering, improve SNR and speech intelligibility, minimize block processing artifacts, and can be implemented in low-power architectures.