The subject of the talk will be the challenges of establishing an R&D portfolio of projects. Some of the trends over the past few decades will be reviewed. Then a mathematical formulation of an optimization model designed to select projects for inclusion in an R&D portfolio, subject to a wide variety of constraints (e.g., capital, headcount, strategic intent, etc.), will be presented. The model is similar to others that have previously appeared in the literature and is in the form of a mixed integer programming (MIP) problem known as the multi-dimensional knapsack problem. Exact solutions of such problems are generally difficult, but can be accomplished in reasonable time using specialized algorithms. Two important issues related to the formulation of project selection models will be discussed in some detail. These issues are: (1) the partial funding and implementation of projects, and (2) the assignment of a quantitative measure of value to the proposed projects.