The aim of this study is to survey the optimization models and methods for supply chain design problems considering the concepts of sustainable development. Supply chain design is one of the most significant issues in supply chain management. The mathematical models in the field of facility location, logistics, supply chain design and strategic planning have been incorporating more and more features of the real-life applications, such as such as collaborative supply chain, supplier selection, dynamic aspect, uncertainty and risk management. Although sustainable development is one of the most challenging features to be taken into account, it is yet poorly considered in the OR models and almost not mentioned in the existing reviews. We will develop the following issues: (i) the constituent parts (economic, environmental and social factors) and ingredients of sustainable development that are included in the mathematical models, (ii) the consequences of considering sustainable development factors on mathematical modeling and optimization methods, (iii) applications in various economic sectors.