Symmetry is an important feature of almost all shapes: nearly every man-made object contains at least one plane of perfect symmetry and most natural objects exhibit near-perfect symmetries. However, symmetry information has been underutilized in computer graphics. In this thesis we will analyze both the perfect and the imperfect symmetries of 2D and 3D models and define a symmetry transform that captures all planar symmetries. We then examine some applications that can benefit from symmetry information such as alignment, completion, shape matching, segmentation, automatic viewpoint selection and remeshing.