Under the assumption of noncircular signals, the conventional linear beamforming technique only utilizes the covariance matrix of the observation vector from the antenna array. However, in the area of modern communication, many artificial modulation signals have noncircularity property, i.e., the observation vector not only has the covariance matrix but also has the conjugated covariance matrix. The WL beamforming technique is proposed as a new technique under the scenario of noncircular signals, which is achieved by defining an extended observation vector consisted by the observation vector and its conjugated version, and obtaining a extend weight vector after constructing an objective function and constraints. In contrast with the conventional beamforming technique, the WL beamforming technique for the reception of noncircular signal has an obvious improvement. In recent years, the WL beamforming technique has been the focus of research at home and abroad. In this paper the definitions of circular and noncircular are introduced, the array model, the minimum variance distortionless response beamformer and various WL beamforming algorithms are presented. Finally, the future research directions are prospected.