During the last decade nonlinear anisotropic diffusion models have shown to be powerful methods not only in image processing. Moreover these methodologies can be adopted to other areas in computer vision. On the level of the continuous model one can study the qualitative aspects and properties whereas approved discretization schemes are at hand for an efficient implementation. In this paper we discuss several anisotropic diffusion methods and outline a novel technique for geometric surface processing. Moreover we will show how the solution process can be accelerated significantly by using texture hardware of modern graphics cards, making use of the much better memory bandwidth and the built-in parallelism.