The increasing importance of supply chain management (SCM) is forcing organisations to reconsider and improvise their purchasing-related matters. In lieu of that, the supplier selection process plays an important role in purchasing activity. The supplier selection process has undergone significant changes in the past forty years. These changes have been beneficial to both the purchasing clients and the suppliers. The supplier selection decision making process involves multiple criteria comprising both qualitative and quantitative aspects. Sometimes, there might be some contradictions between tangible and intangible criteria which may necessitate a trade-off between conflicting criteria. This paper provides an overall picture of research on supplier selection problems and supplier selection practices. Different selection criteria, emerging issues of supplier selection and the solutions for these problems are summarised. This review shows that the application of a structured decision making technique is important, especially under the complex conditions that include both qualitative and quantitative criteria.