This work covers some of the newly discovered properties of the Si-Ge system from a scientific point of view, not forgetting its technological relevance. After the Introduction, where the general features of the growth of Ge on Si are briefly covered, Chap. 1 focuses on the elastic properties of GeSi quantum dots and collects results. In Chap. 2 the study is extended to more than one dot, to reveal their mutual interaction. It is worth to study, in Chap. 3, the effect of a further deposition of Si on an already formed Ge-on-Si system, because of the potential technological application. Later, Chap. 4 presents an important part, namely the study of Ge/Si when the Si substrate is artificially patterned. Here, a total-energy scheme, able to predict the critical volume for island nucleation and shape transition, is extended to quantum dots grown on patterned substrates. Finally, Chap. 5 tackles the problem of mixing between Ge and Si, and gives some theoretical predictions for realistic Ge/Si islands. Due to their relevance, App. 1 reviews the major experimental techniques available to pattern Si substrates.