STM allows to follow dynamical changes on surfaces directly in real space. In particular, diffusion and decay of nanoislands and diffusion of single atoms can be followed on the time scale of the changes. Though original work [1] could be well described within a framework of mean-field theory, more recently the influence of the surface state has been found in several instances. On fcc(111) surfaces the fast decay of stacks of islands originally attributed to the surface state [2] was shown to be of different origin [3]. However, the motion of single atoms and dimers [4] as well as the slow decay of an island [5] were shown to be indeed related to the surface state. Furthermore, the increased diffusivity and reduced decay of small copper islands on Ag(100) will be discussed [6].

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