AbstractThe purpose of this paper is to review various structures of the project-selection problem with discrete multiattribute utility. The approach of maximizing the utility for project selection is discussed where the utility function cannot be measured on a continuous scale. The review includes reference to models of uncertainty versus certainty, and to models assuming the existence of dependence and complementary relations among projects versus independent projects. Project selection in hierarchical organizations with a large number of projects and group decisions is also referred to. The various types of models are formulated and analysed, including applications in the areas of water resources, R&D and nuclear plant location. Finally, directions for future research are suggested.