the computational approximation of solutions of complex systems such as the navier-stokes equations is often a formidable task. for example, in feedback control settings where one often needs solutions of the complex systems in real time, it would be impossible to use large-scale finite element or finite-volume or spectral codes. for this reason, there has been much interest in the development of low- dimensional models that can accurately be used to simulate and control complex systems. we review some of the existing reduced-order modeling approaches, including reduced-basis methods and especially methods based on proper orthogonal decompositions techniques. we also discuss a new approach based on centroidal voronoi tessellations. we discuss the relative merits and deficiencies of the different approaches and also the inherent limitations of reduced-order modeling in general.