Complex surfaces and solids are produced by large-scale modeling and simulation activities in a variety of disciplines. Productive interaction with these simulations requires that these surfaces or solids be viewable at interactive rates - yet many of these surfaces/solids can contain hundreds of millions of polygons/polyhedra. Interactive display of these objects requires compression techniques to minimize storage, and fast view-dependent triangulation techniques to drive the graphics hardware. In this paper, we review recent advances in subdivision-surface wavelet compression and optimization that can be used to provide a framework for both compression and triangulation. These techniques can be used to produce suitable approximations of complex surfaces of arbitrary topology, and can be used to determine suitable triangulations for display. The techniques can be used in a variety of applications in computer graphics, computer animation and visualization.