This paper summarizes an analysis of penalty and multiplier methods for constrained minimization, contained in Refs. [1-3]. We describe global convergence and rate of convergence results for multiplier methods, as well as a global duality theory for nonconvex problems. A main qualitative conclusion is that multiplier methods avoid to a substantial extent the traditional disadvantages of penalty methods (ill-conditioning, slow convergence) while retaining all of their attractive features.