Sometimes a subset of the pairwise distances determined by a point set suffices to uniquely reconstruct all pairwise distances, and hence the configuration of the points in the $d$-dimensional space. In this case we say that the geometric graph (or framework), in which the vertices are the points and the known distances are the edges, is globally rigid. Understanding global rigidity is useful in several applications, e.g. in sensor network localization and molecular conformation. We shall give a survey on the results that lead to a partial characterization of globally rigid graphs and also illustrate the proof methods which come from different areas of mathematics.