Combinatorial optimization problems serve as models for a great number of real problems, and are studied in order to construct algorithms that are effective in terms of complexity and of the quality of the solutions returned. This chapter begins approximation algorithms with performance guarantees, it refer readers who want information on the other approaches to some publications and the references that they contain. The chapter contains a general presentation of multicriteria problems in combinatorial optimization, and tackles notions of optimality and of complexity. It presents four general approaches to polynomial approximation with performance guarantees. Furthermore, each approach is illustrated with an example from various publications. There are four of these approaches: the criteria weighting approach; the simultaneous approach; the budget approach; the Pareto curve approach.