Polygonal models currently dominate interactive computer graphics. This is chiefly because of their mathematical simplicity: polygonal models lend themselves to simple, regular rendering algorithms that embed well in hardware, which has in turn led to widely available polygon rendering accelerators for every platform. Unfortunately, the complexity of these models, which is measured by the number of polygons, seems to grow faster than the ability of our graphics hardware to render them interactively. Put another way, the number of polygons we want always seems to exceed the number of polygons we can afford. Polygonal simplification techniques offer one solution for developers grappling with complex models. These methods simplify the polygonal geometry of small, distant, or otherwise unimportant portions of the model, seeking to reduce the rendering cost without a significant loss in the scene's visual content. The article surveys polygonal simplification algorithms, identifies the issues in picking an algorithm, relates the strengths and weaknesses of different approaches, and describes several published algorithms.