Fidgety particles on surfaces: how do they jump, walk, group, and settle in virgin areas?

This article is aimed at describing the history and current status of surface diffusion, its vital importance in diverse surface phenomena and numerous industrial applications, the recent significant progress in its understanding, and, in particular, many unsettled questions concerning surface diffusion mechanisms. From the fundamental point of view, the interest in surface diffusion and, at the same time, the difficulties in its understanding, stem primarily from the collective (many-body) nature of this phenomenon. On the practical side, the importance of the knowledge of the physics behind surface diffusion is becoming increasingly crucial in the coming era of nanotechnology, which will bring an unprecedented level of miniaturization in electronics and a broad employment of various nanomaterials.