Binaural beamforming technology, which is based on the auditory perception of both ears, uses a wireless data connection to exchange data between the right-side and the left-side hearing aids. Over the years, several multichannel speech enhancement algorithms have been used in the hearing aid industry. For example, beamforming algorithms work by keeping a target signal undistorted while attenuating the noise fields (such as diffuse noise or white noise) and the interferers from different directions. Fixed and adaptive algorithms of this nature have been under active investigation by the hearing aid industry. Although binaural beamforming hearing aids designs have shown better performance than single-channel based hearing aids or bilateral hearing aids, the performance of binaural beamforming still suffers from errors in the direction of arrival estimates, i.e., errors which occur when the right set of steering vectors is used in a beamformer design but the target signal source is not located at the direction considered in the design. Therefore, this thesis is devoted to find and propose structures showing more robustness to errors in the direction of arrival estimates. The focus is mainly on the Generalized Sidelobe Canceller (GSC) structure and several binaural beamforming algorithms and configurations are proposed in this thesis as alternatives for the fixed beamformer and blocking matrix units of the GSC. The proposed algorithms show promise of providing wider notch and/or wider beam possibilities, as well as providing greater noise reduction and superior adaptive null positioning capabilities. The algorithms proposed in this thesis were simulated in MATLAB using recorded signals and data provided by a hearing aid firm, to assess their utility for improving hearing aid performance. The results demonstrated a superiority over algorithms currently in use in industry.