Shape registration and, more generally speaking, computing correspondence across shapes are fundamental problems in computer graphics and vision. Problems from this area show up in many diff erent variants such as scan registration, deformable shape matching, animation reconstruction, or fi nding partial symmetries of objects. Computing correspondences is a main prerequisite for higher level shape processing algorithms, such as building statistical models, non-local denoising, or inverse procedural modeling. Our tutorial addresses correspondence problems in geometric shapes. We will look at the problem from two different perspectives: In the first part of our tutorial, we will motivate the problemand explain the problem structure (formal models for shape matching), its variants (partial vs. complete matching, deformable vs. rigid, etc) and specific challenges (such as noise, incomplete data, and statistical descriptions thereof). In the second part, we will look at algorithms for solving these problems, and at applications of these. Again, we will focus on the main ideas and principles. Our overall goal is to give the attendee a “coordinate system” of the fi eld, to convey the main problem structure and the main approaches to solve the problem, as well as open questions and research challenges. Topics covered will include rigid and deformable shape matching, local and global correspondence algorithms, as well as symmetry detection and applications.