Multiresolution meshes are a common basis for building representations of a geometric shape at different levels of detail. The use of the term multiresolution depends on the remark that the accuracy (or, level of detail) of a mesh in approximating a shape is related to the mesh resolution, i.e., to the density (size and number) of its cells. A multiresolution mesh provides several alternative mesh-based approximations of a spatial object (e.g., a surface describing the boundary of a solid object, or the graph of a scalar field). A multiresolution mesh is a collection of mesh fragments, describing usually small portions of a spatial object with different accuracies, plus suitable relations that allow selecting a subset of fragments (according to user-defined accuracy criteria), and combining them into a mesh covering the whole object, or an object part. Existing multiresolution models differ in the type of mesh fragments they consider and in the way they define relations among such fragments. In this chapter, we introduce a framework for multiresolution meshes in order to analyze and compare existing models proposed in the literature on a common basis. We have identified two sets of basic queries on a multiresolution meshes, that we call selective refinement and spatial selection. We describe two approaches for answering such queries, and discuss the primitives involved in them, which must be efficiently supported by any data structure implementing a multiresolution mesh. We then describe and analyze data structures proposed in the literature for encoding multiresolution meshes.