Abstract: Whereas mechanics theories for isotropic materials have been nearly matured, essentially only the linear elasticity theories for anisotropic composite materials are well established. All of the other mechanical behaviors of the composites are not well understood. Specifically, the failure and strength analysis for the composites still remains to be one of the greatest challenges in solid mechanics. During the last 25 years, in order to advance the development in the mechanics of composite materials, this author has established a series of analytical theories. They include the constitutive and internal stress calculation theory, named Bridging Model, for composites reinforced with continuous or short fibers or particles, the true stress theory for converting a homogenized stress of the matrix in a composite into a true value, the failure criteria for matrix failures established on a physics based principle, the interlaminar matrix stress modification method for predicting interlaminar fracture or delamination of any laminated structure, and the incremental constitutive relation for hyperelastic materials. Based on these theories, almost all of the failure problems of two-phase composites can be efficiently resolved through analytical formulae, as long as void contents in the composites can be neglected. Amongst, Bridging Model has been known world-widely, and more than 250 publications have been made by people other than the author’s group using Bridging Model as a theoretical tool. Furthermore, the others’ publications based on the matrix true stress theory have reached a number of 20, although this theory has been established only recently by the author. A brief summary on the establishment of the author’s theories and how to apply them to resolve challenging problems in composites and their structures is presented in the paper.