Shorter product life due to technology development and changing customer needs requires optimal supply chain management and structuring. Achieving this optimization brings productivity to the organization. A sustainable and reliable supply chain (S&RSC) as an emerging paradigm, with a comprehensive view, leads the supply chain network design (SCND) issue to the desired situation. This study, as part of an emerging theme, presents a systematic review and classification of 42 articles at the intersection of sustainability, reliability, and supply chain network design. In this regard, in a historical course, the four concepts of green supply chain, socially responsible supply chain, sustainable supply chain, and reliable supply chain in the form of four structures of history and definition, deriver and importance, substrate and practice, evaluation, and implementation are discussed. The result of the review shows that the articles that study the integration of sustainability and reliability in SCND are vibrant and rapidly growing in various industries. Developing countries and manufacturing companies with the largest number of articles have been the research fields of the studies. Most of the studies have considered the structure of the supply chain as a forward flow. The key contribution of this review is the development of a comprehensive framework of S&RSC from the conceptual point of view, elements, assessment tools, and its implementation context. The present review can serve as a guide for various stakeholders. In particular, practitioners and policymakers can effectively develop their own strategies and policies to advance the sustainable-reliable program.