Abstract: The static and dynamic mechanical response characteristics and macro and micro failure characteristics of brittle ceramics are the basis for the study of the constitutive model of brittle materials. A reasonable constitutive model can accurately predict the impact response and failure behavior of brittle materials. The numerical simulation method based on the constitutive model can provide support for the analysis of the impact failure law of ceramic materials. In this paper, the static and dynamic loading tests of brittle ceramic materials are reviewed, and the macro and micro failure mechanisms of materials under different loading conditions are analyzed. The constitutive model of impact response and failure behavior of brittle ceramics is introduced from three aspects: macroscopic phenomenological, mesoscopic physical mechanism and multi-scale coupling calculation. The application of constitutive model in numerical simulation technology of impact response of brittle ceramics is summarized. Finally, in view of the shortcomings of the current research on the failure mechanism and constitutive model of brittle ceramics, some suggestions on the future research direction are put forward.