Many applied-science fields like medical imaging, computer graphics and biology use meshes to model surfaces. It is a challenging problem to determine whether, how and to what extent such surfaces correspond to each other, e.g. to see whether they are differently parametrized views of one object, or whether they indicate movement of part of an object with respect to its other parts. In this talk we will show how the Uniformization theory can be used to establish correspondences between simply-connected surfaces. We will present an algorithm for automatically finding corresponding points between two discrete surfaces (meshes). The algorithm is based on the observation that the correspondence problem between nearly isometric surfaces is a low dimensional problem in practice, which is well characterized by the Mobius group of fractional linear transformations.