The sustainability of an entire supply chain and the final product is affected by the sustainability performance of each partner in the chain. The buyer-supplier relationship plays an important role in improving sustainability of the supply chain. This paper aims to provide a systematic review of existing literature on the adoption of sustainability practices through supply relationships. To this end, a structured literature review has been carried out that analyzes published research, evaluates contributions, and summarizes the results. The authors selected only those papers that discussed sustainability practices adoption and relationship management in the supply chain. An in-depth analysis of the supply chain and its processes reveals that a buyer-supplier relationship should be determined on the basis of the capability and capacity of the partner (supplier). In cases where the supplier firm lacks capability or capacity, the focal firm may decide to help or extend support. The buyer-supplier relationship starts with selecting suppliers based on their sustainability standards. In order to give a better understanding of the mechanisms active, and processes involved in the development of a sustainable supply chain, the authors offer a conceptual model. The study also identifies indicators, enablers and barriers to a sustainable supply chain.