Over the last years, kernel methods have established themselves as powerful tools for computer vision researchers as well as for practitioners. In this tutorial, we give an introduction to kernel methods in computer vision from a geometric perspective, introducing not only the ubiquitous support vector machines, but also less known techniques for regression, dimensionality reduction, outlier detection, and clustering. Additionally, we give an outlook on very recent, non-classical techniques for the prediction of structure data, for the estimation of statistical dependency, and for learning the kernel function itself. All methods are illustrated with examples of successful application from the recent computer vision research literature.