Morphological changes on surfaces have been followed in real time by scanning tunnelling microscopy on the time scale of seconds to days. This "on-site on-time" mode has been employed for the observation of decay, motion, coalescence, and shape fluctuations of islands on the low-indexed faces of Ag, Cu, Pt, and Au. For island changes under well-defined conditions, well-established theories are adapted to identify atomic processes and extract quantitative information on diffusion parameters important for growth and stability of nanostructures, such as energies and prefactors. Extension of the "on-site on-time" approach to atoms, dimers, etc. and to dislocations is outlined.