Deformation is a key component in many applications including virtual surgery and the animation of digital characters in the movie industry. Previous deformation methods either require non-intuitive ways of specifying the deformation or have been too expensive to compute in real-time. We focus on three methods 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, we conclude with our work on creating deformations described by collections of points using Moving Least Squares.