Ceramic matrix composites with environmental barrier coatings (CMC/EBCs) are the most promising material solution for hot section components of aero-engines. It is necessary to access relevant information and knowledge of the physical properties of various CMC and EBCs, the characteristics of defects and damages, and relevant failure mechanisms. Then, effective failure prediction models can be established. Individually assessing the failure of CMC and EBCs is not a simple task. Models considering the synergetic effect of coating properties and substrate fibrous architecture are more reasonable and more challenging. This paper offers a review and a detailed description of the materials features, failure mechanism, and failure modeling for both CMC substrate and EBC coatings. The various methods for failure analyses and their pros and cons are discussed. General remarks on technical development for failure modeling are summarized subsequently.