In recent decades, surface and interface physics has become an increasingly important subdiscipline within the physics of condensed matter as well as an interdisciplinary field between physics, crystallography, chemistry, biology, and materials science. There are several driving forces for the development of the field, among them semiconductor technology, new materials, epitaxy and chemical catalysis. The electrical and optical properties of nanostructures based on different semiconductors are governed by the interfaces or, at least, by the presence of interfaces. A microscopic understanding of the growth processes requires the investigation of the surface processes at an atomic level. Elementary processes on surfaces, such as adsorption and desorption, play a key role in the understanding of heterogeneous catalysis. During the course of the surface investigations, it has been possible to observe a dramatic progress in the ability to study surfaces of materials in general, and on a microscopic scale in particular. There are two main reasons for this progress. From the experimental point of view it is largely due to the development and availability of new types of powerful microscopes. Sp- tacular advances in techniques such as scanning tunneling microscopy now allow us to observe individual atoms on surfaces, and to follow their paths with a clarity unimaginable a few years ago. From the theoretical point of view (or rather the viewpoint of simulation) progress is related to the wide availability of computers and the dramatic increase of their power.