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In recent decades, adaptive arrays have been widely used in sonar, radar, wireless communications, microphone array speech processing, medical imaging and other fields. In practical array systems, traditional adaptive beamforming algorithms are known to degrade if some of exploited assumptions on the environment, sources, or antenna array become wrong or imprecise. Therefore, the robustness of adaptive beamforming techniques against environmental and array imperfections and uncertainties remains one of the key issues. In this paper, we overview a recently emerged approach to robust adaptive beamforming using worst-case performance optimization.