Shape is important in GI Science because the shape of a geographical entity can have far-reaching effects on significant characteristics of that entity. In geography we are mainly concerned with two-dimensional shapes such as the outlines of islands, lakes, and administrative areas, but three-dimensional shapes may become important, for example in the treatment of landforms. Since the attribute of shape has infinitely many degrees of freedom, there can be no single numerical measure such that closely similar shapes are assigned close numerical values. Therefore different shape descriptors have been proposed for different purposes. Although it is generally desirable for a shape descriptor to be scale invariant and rotation invariant, not all proposed descriptors satisfy both these requirements. Some methods by which a shape is described using a single number are described, followed by a discussion of moment-based approaches. It is often useful to represent a complex shape by means of a surrogate shape of simpler form which facilitates storage, manipulation, and comparison between shapes; some examples of commonly used shape surrogates are presented. Another important task is to compare different shapes to determine how similar they are. The article concludes with a discussion of a number of such measures of similarity.