This thesis is committed to the study of nanometer scale surface processes involved in the formation and evolution of self-organized semiconductor quantum dots. The aim is to contribute to a better understanding of the mechanisms influencing the final shape and composition of as-grown quantum dots, as well as those exposed to post-growth treatments (annealing and overgrowth), since these determine in great extent the optic and electronic characteristics of the quantum dots. The whole investigation conducted in the frame of this dissertation was performed by means of in-situ STM measurements of quantum dots formed on the two most important model semiconductor systems, InAs/GaAs(001) and Ge/Si(001). InAs/GaAs(001) quantum dots grown at high temperature and extremely low flux are investigated. The detailed analysis of high resolution STM images of these dots allows for first time the exact determination of their shape, as well as the precise identification of the facets orientation composing them. This shape is in excellent agreement with recent theoretical predictions, proving that the chosen deposition conditions are close to thermodynamic equilibrium. The low-temperature GaAs overgrowth of these QDs is investigated during the initial stages (1-30 ML). Two regimes appear to dominate the capping, an initial partial dissolution of the QDs followed by a true overgrowth. The generality of this picture is confirmed by experiments done at different overgrowth rates. The observed dependence of the QD evolution on the GaAs flux demonstrates that the observed phenomena are kinetically driven and that the two regimes are governed by different atomic processes. It is noticed that during the overgrowth, the dot dissolution is accompanied by a shape transformation. The different transition shapes adopted by the overgrown dot are clearly identified and a physical interpretation of the atomistic mechanism producing these shape changes is presented. The pyramid-to-dome transition in the Ge/Si(001) system is investigated. The precise pathway of the transition is determined from nanometer-resolution images and can be described as a selective overgrowth of pyramid islands. Based on experimental data and on atomistic arguments derived from recent theoretical investigations, a simple model that captures the essential features of the transformation is also presented. By analyzing both quantum dot semiconductor systems, we demonstrate that the existence (and coexistence) of only two well-defined families of islands (smallshallow and large-steep) as well as the transformations that these undergo during the embedding-passivation process, are general features and do not depend on the particular material system.