Given that wind hazards pose a considerable damage to power system in various countries, researchers have developed methods for disaster prevention to diminish the vulnerabilities. This paper attempts to review the failure analysis procedure under the impact of wind hazards, considering the following attributes: wind field generation method, wind-induced electrical component failure model in transmission system, and building outage prediction model from data-driven view in distribution system. First, we compare the calculation of circulation and translation wind speed, with geographical, temporal and uncertainty factors of wind speed considered. Then, we introduce the wind-induced component failure models derived by wind load calculation and fragility curves. The application of the series reliability model in multiple cluster failures is briefly described. Finally, we summarize the applications of data analysis in building outage prediction models. The reviewed literature contains the statistical learning methods and machine learning methods. It is concluded that the frameworks for component-level failure model and user-level outage prediction model are well established. However, most of the studies still develop two models, separately. Future researchers may target at the hybrid application of both models to better provide fault analysis, prediction and emergency in power system under wind hazards.