Depending on the flight mode, the airflow can either damp aircraft oscillations, or, conversely, the oscillating structure takes energy from the incoming flow, as a result of which a rapid increase in amplitude of oscillations may occur. This dangerous phenomenon has become a significant obstacle to the development of high-speed aviation. Since the 1930s and up to the present time, the efforts of many researchers are aimed at describing the dynamics of this phenomenon, studying its properties and developing measures to prevent it. In the present paper, some existing results on elastic-flexural wing flutter are surveyed. The paper starts from various ways of modeling the elastic-flexural wing flutter. The results on investigations of the elastic-flexural wing flutter phenomenon are reviewed, and several approaches of passive and active flutter suppression methods are described.