The literature of combinatorial optimization, and of related fields such as graph theory. is replete with numerous examples of duality theorems and their applications: the Max-Flow Min-Cut Theorem, Konig-Egervary Theorem, Edmond’s Odd Set Covering Theorem, Hoffman’s Circulation Theorem, Minty’s Painting Theorem, Menger’s Theorem, Dilworth’s Theorem, etc. Our objective in this Chapter is to review a few of these duality results and to give some examples which may be convincing of the usefulness of duality concepts in problem formulation and solution.