Introduction: Recently, there has been an active development of algorithms for adaptive beamforming. Such work is required in order to improve the efficiency of receiving a useful signal, especially in mobile communication systems. This article provides an overview of research on this topic. Papers devoted to the improvement of the classical least mean square algorithm, blind signal separation methods, antenna selection algorithms in MIMO systems and other topics of adaptive signal processing are presented. Practical relevance: Adaptive beamforming is a key development for modern wireless communication systems, in particular 5G. Increasing requirements that impose a limitation on the spectral bandwidth of the signal and its center frequency with limited signal power lead to the strategy of forming a narrow signal transmission beam, thereby increasing the energy efficiency of signal transmission and reducing the overhead associated with the reception of various interference. This article provides an overview of studies on this topic. The results of the analysis of works devoted to the improvement of the classical algorithm for minimizing the mean square error, blind signal separation, antenna selection algorithms in systems of several antennas, and other topics of adaptive signal processing are presented. Discussion: It is shown that the main directions of research are focused on the improvement of classical diagramming algorithms, as well as on the improvement of methods for receiving digital signals in MIMO systems. Algorithms for recognizing the type of signal modulation, an algorithm for blind separation of second-order signals, an improved algorithm for automatic gain control, an algorithm for suppressing noise-like interference, and an algorithm for estimating radiation pattern parameters were also considered.