In recent years, multiresolution modeling has proved to be valuable in 3D geometric surface modeling and computer graphics. It is concerned with the generation, representation, visualization, and manipulation of surfaces at various levels of detail or accuracy in a single model. Applications include fast rendering, level of detail editing, collision detection, scientific visualization, as well as compression and progressive transmission. A widespread example for multiresolution surfaces is the subdivision surface. Starting from very simple primitives, such as cubes or spheres, the user can progressively deform and enrich the surface with tools like, for instance, extrusion, shear or twist. As soon as a coarse level is correctly modeled, the user can refine the model by applying a subdivision pass, and add finer details, tessellate the areas where more features are required, and thus model the shape more and more accurate by using the different levels of refinement of the subdivision surface. Indeed, a major advantage of the subdivision surface is flexibility: the user can modify the shape at any resolution - the deformations at coarser levels are automatically propagated to the finer levels. Multiresolution is also the link between geometric modeling and rendering, providing for instance an appropriate level of detail for a given viewpoint in order to ensure real-time rendering. A simple example, introduced in the 90s, is the progressive polygonal mesh. Starting from a detailed single model, multiple coarser mesh resolutions can be generated by the successive application of an edge collapse operator. Of course, coarser mesh resolutions can be rendered more efficiently, at the expense of lost fine details. All these multiresolution techniques must now be adapted to acquired surface data, since due to the recent advances in 3D acquisition devices, the surfaces are more and more scanned from the real world rather than modeled. A challenging task is to handle the modeling and rendering of the large amount of data usually provided by 3D scanners in real-time. For example, the significant overhead of dealing with the connectivity of polygonal meshes has motivated various researchers to seek for alternative multiresolution surface representations, as for example point-based surfaces. In this talk, we first briefly review some classical surface definitions such as polygonal meshes and spline surfaces. Then, we give further insight in surface definitions that have gained much attention recently as suitable multi-resolution representations, such as subdivision surfaces, implicit surfaces, and point-based surfaces. Our special interest focuses on how these surface representations are adapted for multiresolution modeling and rendering in the above-mentioned applications.Read less <