Supplier selection is considered to be one of the most critical activities of purchasing management in a supply chain. Selecting the right suppliers significantly reduces the purchasing cost and improves corporate competitiveness. Diverse methods have been developed to date, which address the needs of the supplier selection process. This article presents a review of non-deterministic analytical methods reported in the literature for supporting the supplier selection decision. The review is based on an extensive search in the academic literature from 2001 to 2013. A taxonomy of the supplier selection methods is presented by classifying the published supplier selection studies into two major categories as stochastic methods and fuzzy methods. These methods are further divided into individual approaches and integrated approaches. The objective of this research is threefold. First, it classifies the existing supplier selection literature according to the methods employed and determines the most prevalently used approaches, and also highlights main advantages and shortcomings of these approaches. Second, recent trends in supplier evaluation and selection methodologies are examined. Finally, this study identifies the most widely used decision criteria for supplier selection.