The bombardment of the surface of a solid by energetic ions often results in pronounced surface modifications, leading to characteristic topographical features. In this report, the development of specific morphological nanostructures on surfaces under ion irradiation is discussed. The following aspects will be emphasized: (i) on an atomic scale, the generation of isolated defects such as adatoms and surface vacancies due to single-ion impacts, and their possible clustering; (ii) the transition

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... rom such individual defects toward extended morphological features on the surface and suitable scaling relations to describe them; (iii) the formation of highly periodic structures with nanoscale dimensions such as nanodots and "ripple"-like features, and the dependence of these nanostructcures on various ion-irradiation parameters and substrate materials; (iv) the theoretical concepts proposed to model the observed patterns which are thought to be related to (and caused by) the interplay between ion erosion and diffusion of adatoms (vacancies), thus inducing a surface reorganization.