The Capon beamformer, known as the optimal beamformer in suitable case, has the remarkable interferences suppression capability. However, the Capon beamformer is highly sensitive to the model mismatches. Especially when the covariance matrix and desired signal steering vector errors are existed, the performance of beamformer would degrade dramatically, which greatly reduces the robustness of the beamformer. Nowadays, a number of robust adaptive beamforming (RAB) algorithms based on the covariance matrix reconstruction have been proposed. The main idea of these algorithms utilizes the Capon power spectrum integrated in the special region to reconstruct the covariance matrix. In this paper, the signal model of beamforming is introduced firstly, and four typical covariance matrix reconstruction RAB algorithms are expounded based on the Capon beamformer. Finally, the future research directions are prospected.