Geometric Matching in Computer Vision--Algorithms and Open Problems Thomas M. Breuel IDIAP, C.P. 609, 1920 Martigny, Switzerland tmb@idiap.ch In this paper, I review and discuss recent advances in the development of algorithms for solving the kinds of geometric matching problems that occur in computer vision, in particular under bounded error models. I examine both the one-model case (recognition) and the many-model case (indexing), and I discuss some open problems and directions for research.