Surface reconstruction is a problem in the field of computational geometry that is concerned with recreating a surface from scattered data points sampled from an unknown surface. To date, the primary application of surface reconstruction algorithms has been in computer graphics, where physical models are digitized in three dimensions with laser range scanners or mechanical digitizing probes (Bernardini et al., 1999 [1]). Surface reconstruction algorithms are used to convert the set of digitized points into a wire frame mesh model, which can be colored, textured, shaded, and placed into a 3D scene (in a movie or television commercial, for example). In this paper, we discuss some computational geometry preliminaries, and then move on to a summary of some different techniques used to address the surface reconstruction problem. The coming sections describe two algorithms: that of Hoppe, et al. (1992 [2]) and Amenta, et al. (1998 [3]). Finally, we present other applications of surface reconstruction and a brief comparison for some algorithms in this filed emphasizing on their advantages and disadvantages.