To develop national economy and use the water resources and hydropower resources sufficiently, a lot of high arch dams, with the height of more than 200 m, have been and will be built in China. Although arch dams have good mechanical behavior, there is still failure possibility due to the huge water pressure and high stress level in dam, complex topographic and geologic conditions, formidable environment and high intensity earthquake. As one of the three main aspects concerning the safety of high arch dam, the study on global destruction, has been elaborated in the literatures, and research advance in the other two aspects, namely the failure risk and local damage of high arch dams, will be reviewed in this paper. In recent years, the failure risk of high arch dams has been investigated, and the model for identifying dam failure risk factors has been established. It is shown that the foundation deterioration and strong earthquake are the major risk sources for high dam failure. With the fault tree method, the failure mode and failure probability of high arch dams are studied, and the principle for determining failure mode and the method of calculating failure probability are proposed. Meanwhile, the determination principle of acceptable risk standard for high arch dam was proposed, and the acceptable risk rate and the acceptable standard value of various risk losses were given. For the local damage of arch dam, it is pointed out that the local damage belongs to the strength failure at material level. The study on local failure mechanism of arch dam is reviewed, based on the theories that from traditional strength theory to damage mechanics and meso-mechanics theory. Aiming at the cracking, the main pattern of local failure of high concrete dam, the research advances in the analysis methods and cracking criteria for smeared crack model and discrete crack model are summarized, and the research findings of preventive measures for local failure are shown.