Surface diffusion on metals has been a subject of scientific interest for roughly ninety years. During the first forty years of this period it was very hard to do meaningful work because of technical problems – the difficulty of establishing good enough vacuum conditions to maintain a surface clean for measurements. In a few laboratories, mostly industrial, ultrahigh vacuum techniques were already practiced at that time, but this was not the normal course of events. All of this changed after World War II, first with the general adoption of good vacuum practices, and then with the development of more capable techniques for examining kinetic processes that are important on a surface. The first of these techniques was field ion microscopy, invented by Erwin Müller, the first method to provide a direct view of single atoms on a surface. The next important development was the scanning tunneling microscope, devised by Binnig and Rohrer, which established the capability of probing a large scale surface with high resolution. The last major contribution was the progress in theoretical techniques and computer technology, which toward the end of the twentieth century led to the rapid growth of theoretical calculations.

The last forty years have therefore been a time of great progress in our understanding of surface diffusion, especially of metal atoms on metals. These advances have been spread over the scientific literature, and there has been no overview of the entire field, which is what we are trying to provide here.