All activities in a supply chain are to provide market demand by providing products with the highest quality, minimum price and at the right time to the customers. Given the essential role of suppliers in cost, quality, service and other standards, in achieving the goals of the supply chain, suppliers are an essential part of an organization with a significant impact on the organizational performance. Due to these various effects, it is necessary to use precise and efficient techniques for assessing and select suppliers and assign orders to them. Thus, researchers have suggested a wide range of techniques by to examine the issue of selecting suppliers. Therefore, this study first deals with the problem and the process of choosing suppliers. Then, some techniques and studies done for each step of the supplier selection process are presented. As in the real world the issue of choosing suppliers in practice often faces uncertainty and constraints for the buyer and suppliers, at the last stage of the supplier selection process, only a few studies are conducted on choosing suppliers in a multivariate source-finding mode in an uncertainty environment. Finally, summaries and suggestions are presented for future research.