Physical models of deformable objects proved to be valuable for a range of applications in graphics. Variational problems provide control over deformable objects and have been used to develop tools for efficiently editing complex shapes and for creating realistic motions. However, solving such a variational problem comes at a significant computational cost. In this talk, I will show how model reduction techniques can be used to get interactive control of deformable objects in two scenarios: editing of shapes and creating animations from keyframes.