Icing, a phenomenon that occurs in extremely cold weather, poses significant challenges to the operation and reliability of overhead transmission line (OHTL). Consequently, drawing upon the comprehensive analysis of icing hazard, the primary objective of this paper is to provide a comprehensive overview of the existing research on fault prediction. Firstly, the paper encompasses historical icing accidents to grasp an understanding of the potential hazard that can lead to mechanical damage, electrical damage, and maintenance issues caused by icing. Secondly, according to the nonlinear relationship between the line fault risk and the ice wind load, the current research progress and technical difficulties of fault prediction are discussed in detail. Finally, this paper outlines the prospective future directions for predicting icing fault on OHTL. In the future, it is possible to quantitatively calculate the fault risk of icing and establish an emergency decision-making model for ice melting with the goal of minimizing the risk of power system, so as to provide decision-making guidance for efficient ice melting.