The research in this thesis is emphasized on the investigation of optimization techniques for robust beamforming (against large steering direction errors and interferences) and antenna selection. This thesis studies the robust beamformers based on worst-case performance optimization in the presence of large steering direction errors and found that their output signal-to-interference-plus-noise ratios (SINRs) are limited. Hence, iterative robust minimum variance beamformers are proposed to improve the output SINRs by using a small uncertainty sphere (and a small flat ellipsoid) to search for the desired array steering vector iteratively. The thesis studies the robust beamformers based on worst-case performance optimization and the covariance matrix taper approach in scenarios with low snapshots and large steering direction errors and found that they lack beampattern control which can lead to drastic output SINR degradation in the presence of unexpected or strong moving interferences. Thus, an adaptive beamforming framework based on the use of a set of beampattern shaping constraints is proposed to achieve robustness against large steering direction errors and strong interferences that move during which the beamforming weights are applied. The proposed framework possesses adaptive interference rejection and direct sidelobe suppression capabilities which are controlled automatically in different scenarios without ambiguity by a weighing ratio.