Hearing impairment is a prevalent, world-wide ubiquitous problem. An increasing number of people suffer from perceptual hearing loss which cannot be remedied by mere amplification, but rather calls for advanced speech enhancement functionality offering increased speech intelligibility. This project focuses on speech enhancement for hearing-aid applications with one or two microphones available. In specific noise reduction and speech quality improving functionality is attended. In order to measure speech quality, a survey of speech-assessment techniques lay the basis for the choice of signal-to-noise ratio (SNR) and weighted spectral slope measure (WSSM) as preferred measures of noise reduction and speech distortion, respectively. For completeness, two single-channel noise reduction techniques are investigated. Spectral subtraction, which is a well-documented, classical method for noise reduction, and the signal subspace approach. Despite its computational complexity, the signal subspace approach is found uncompetitive. However, by extending the method to multiple channels, the GSVD-based multi-channel Wiener filter is formulated. This method relies on long-term stochastic estimates and show robust to different noise types compared to single-channel methods, fixed and adaptive beamforming. However, the multi-channel Wiener filter relies on a good voice activity detector (VAD). Motivated by the observation, that the noise reduction problem often is shifted towards a noise estimation problem, two methods for noise estimation are investigated. For spectral subtraction, a method of minimum-statistics tracking and, for all methods, a log-energy-based VAD. Both methods prove suitable for additive white and pink noise, but fails in babble noise setups. Simulations using reverberated environments reveal that little noise reduction and reduced speech distortion is attained. A combined dereverberation and noise reduction method is investigated. It show no significant improvement. The complexity of the multi-channel Wiener flter is examined and, with acceptable performance degradation, a recursive GSVD-based implementation in 32 bit floating-point precision is created, running in real time on a Pentium-based workstation.