Catastrophic rupture of brittle solids is very significant in, such as earthquakes, landslides, pillar failures, the movement of underground works and instability of structure. However, there is still a limited understanding of the triggering mechanism in natural catastrophic ruptures and their prediction. The principal purpose of this paper is to present a comprehensive demonstration on four key points, i.e., mechanism of catastrophic rupture, effects of heterogeneity, localization and physical precursors. Based on the analysis of the progress on them, we propose the current difficulties and potential strategies in research of damage nonlinear evolution, localization and catastrophic precursors.