This paper reviews the history and current situation of the research on the glaze icing process and typical galloping characteristics of transmission lines. Firstly, the effects of wind speed, ambient temperature, supercooled water content in air, droplet diameter, wire transmission current and water film thickness on the glaze icing process are emphatically analyzed. Secondly, two research methods of experimental observation and numerical simulation are introduced, and the mechanism of glaze icing on the transmission line is discussed from three aspects of thermodynamics, fluid mechanics and electric field. Thirdly, the typical crescent-shaped and fan-shaped icing sections of transmission lines are discussed. The aerodynamic characteristics of glaze icing on the transmission line are analyzed from four aspects : wind attack angle change, icing thickness, turbulence intensity and average airflow velocity. The glaze icing process of transmission lines is divided into three stages, namely, only water film on the surface of transmission lines, thin icing on the surface of transmission line and thick ice layer on the surface of transmission lines. The mechanism of cable-like wind-rain excitation, vortex-induced vibration, classical theory of icing galloping of transmission line and other theories of icing galloping of transmission line are expounded in turn. Then, the differences between glaze-icing process of transmission lines and airfoils of are analyzed from three aspects of wind speed, water film flow and conductor motion. Finally, on the basis of summarizing the previous research results of glaze icing on transmission lines, the model of glaze icing on transmission lines and its possible research direction in the future are pointed out.