The world is becoming more and more a global marketplace and the global environment is forcing companies to take almost everything into consideration at the same time. Increase flexibility is needed to remain competitive and respond to rapidly changing markets. In this context, supplier selection represents one of the most important function to be performed by the purchasin- g department. The supplier selection is a multi-criterion problem which includes both qualitative and quantitative factors (criteria). In order to select the best suppliers it is necessary to make a trade off between these tangible and intangible factors some of which may conflict. This report deals with the 'supplier selection problem', where a state of the art is presented. We summarize the different selection criteria, the various problems of suppliers selection and the existing methods to solve the problem. A numerical example is presented to 1- illustrate the different selection criteria and methods and 2- to compare the advantages and the disadvantage of the selection methods.