In the first part of the talk, I will first give a brief overview of recent research in my group on 3D shape analysis, modeling, and animation. The second part will be devoted to symmetry. I will discuss our work on finding and enhancing partial and approximate symmetries in 2D and 3D geometry using a suitable symmetry transformation space. In this space, symmetry detection can be formulated as a clustering operation. Symmetrization, a method for enhancing symmetries in geometric models, is implemented as an optimization process that couples the spatial domain and the symmetry transformation space to drive a constrained deformation model that pulls the shape towards symmetry. I will derive these methods step-by- step on simple 2D examples and show various applications where symmetry can be utilized such as complexity reduction, structure analysis, and correspondence computation.