The usage of textile structures as a reinforcement for polymer composites became essential in many industrial applications in, for example, the marine and aerospace industries because of their favorable stiffness and strength to weight ratio. Determination of elastic properties and failure behavior of textile reinforced composites is vital for industrial design and engineering applications. This paper aims to present a review of numerical and analytical models for elastic, thermal, and strength/failure analysis of 2D reinforced woven composites. Major modeling techniques and approaches are presented. A state of the art review of woven fabric composites is presented starting from earlier one-dimensional models to recent three-dimensional models. The intention is not to give a detailed analysis of the mathematical approaches to the models discussed, but rather to inform researchers about the main ideas of previous works. This review article cites 122 references.