The problem of representing 2 1⁄2 dimensional surfaces defined at a set of randomly located points by means of triangular grids is considered. Such representations approximate a surface as a network of planar, triangular faces with vertices at the data points. In the paper we describe different models and data structures for encoding triangular grids. Since Delaunay triangulation provides a common basis for many models of 2 1⁄2 D surfaces, we review its basic properties and we describe the most important approaches to its construction. Hierarchical surface models are also presented, which are based on nested triangulations of the surface domain and provide variable resolution surface representations. An algorithm is described for building a hierarchical description of a nested triangulation at different levels of abstraction. Finally, the 3D surface reconstruction problem is briefly discussed.