Efficient representation of geometric models is essential in many applications in Geometric Design and Computer Graphics. In this talk, I will discuss two general approaches for efficient representations of geometric models--adaptive representation and sparse representation. For adaptive representation, we propose splines over T-meshes. We discuss some theoretic issues such as dimension calculation and basis constructions of the spline spaces. We then apply splines over T-meshes in adaptive modeling of geometric models. For sparse representation, we apply the L_1 optimization technique in surface denoising and 3D printing.  Further research problems are also discussed