The ability to identify similarities between shapes is important for applications such as medical diagnosis, object registration and alignment, and shape retrieval. In this paper we present a method, the Curvature Map, that uses surface curvature properties in a region around a point to create a unique signature for that point. These signatures can then be compared to determine the similarity of one point to another. To gather curvature information around a point we explore two techniques, rings (which use the local topology of the mesh) and Geodesic Fans (which trace geodesics along the mesh from the point).We explore a variety of comparison functions and provide experimental evidence for which ones provide the best discriminatory power. We show that Curvature Maps are both more robust and provide better discrimination than simply comparing the curvature at individual points.