Deformation is a key component in many applications including virtual surgical simulation and the animation of digital characters in the movie industry. Previous deformation methods have led to non-intuitive ways of specifying the deformation or have been too expensive to compute in real-time. This talk will focus on three methods we have developed for creating intuitive deformations of 3D shapes. The first method is a new, smooth volumetric subdivision scheme that allows the user to specify deformations using conforming collections of tetrahedra, which generalizes the widely used Free-Form Deformation method. The next technique extends a fundamental interpolant in Computer Graphics called Barycentric Coordinates and lets the user manipulate low-resolution polygon meshes to control deformations of high-resolution shapes. Finally, the talk will conclude with some of our recent work on creating deformations described by collections of points using a technique called Moving Least Squares.