Throughout this book several bicriteria sum optimization problems such as minimum spanning tree problems, shortest path problems, minimum cost flow problems, knapsack problems and global minimum cut problems are considered. For each of those problems the size of the non-dominated sets and the polynomial solvability is investigated. Examples for problems having polynomially bounded non-dominated sets, which are NP-hard to compute, are also presented. Additionally, some general conditions guaranteeing that the Pareto set of such sum optimization problems can be computed in polyomial time are presented.