Multiresolution terrain models describe a topographic surface at various levels of resolution. Besides providing a data compression mechanism for dense topographic data, such models enable us to analyze and visualize surfaces at a variable resolution. This paper provides a critical survey of multiresolution terrain models. Formal definitions of hierarchical and pyramidal models are presented. Multiresolution models proposed in the literature (namely, surface quadtree, restricted quadtree, quaternary triangulation, ternary triangulation, adaptive hierarchical triangulation, hierarchical Delaunay triangulation, and Delaunay pyramid) are described and discussed within such frameworks. Construction algorithms for all such models are given, together with an analysis of their time and space complexities.