We investigate here the heteroepitaxy of silicon-germanium (SiGe), a system which is commonly regarded as the stereotype of semiconductor epitaxy. While this system has already attracted a tremendous amount of attention due to its applications for band-gap engineering in microelectronic industry, the major challenge facing the development of new SiGe-based devices remains the con- trollable epitaxial growth of self-assembled nanostructures. It is well-known that SiGe follows a Stranski-Krastanov growth mode, which proceeds via the growth of bi-dimensionnal layers followed by the growth of three-dimensional islands. Under this generic “Stranski-Krastanov” designation, several different behaviors can be identified. An overall understanding of all these behavior is still partially missing due to the complexity and the interplay of kinetics and energetic driving forces, preventing the development of new devices.In this work we focus on the self-assembly of SiGe nanostructures following the quest of light emission for integrated Si-based photonic, optoelectronic and nanoelectronic devices.Even if the innovation in Si-based devices has been boosted recently by the development of ultra-thin body fully depleted silicon on insulator transistors, a real breakthrough would be the demonstration of light emission and/or absorption by group IV elements since it allows the conve- nient integration into the nowadays semiconductors.In this work we first demonstrate the different growth regimes of strained films, i.e. instability versus nucleation regimes. We develop a model which resolves the race of these two growth pathways and unveil the mechanisms of different modes of morphological evolution driven by elasticity.In the second part, we examine in details the natural self-organisation of coherent islands. The direct elastic effect induces repulsion between coherent islands. However, the strain-dependent surface energy which has been overlooked previously in analysis of the island-island interaction is revealed to cause an attraction between islands. It may compensate the direct elastic repulsion during the initial state of nucleation and lead to the clustering of coherent islands.In a third part we study the influence of miscut steps of vicinal substrate on the formation and self-organisation of islands. We demonstrate that the strain relaxation anisotropy produced by the step edges, is at the origin of the instability elongation perpendicular to steps. Quantitative agreement between the instability elongation and the anisotropy of strain relaxation is found, which deepens the understandings of hetero-epitaxial growth on vicinal substrate.In the fourth part we develop a new process based on Ge condensation during thermal oxidation of dilute SiGe. The kinetics of SiGe condensation process is investigated and the fully strained SiGe epilayer is fabricated via this particular condensation process. This process can be applied in fabrication of SiGe core-shell nanostructures, for which the direct deposition and growth process is found to be cumbersome in terms of the control of morphology and composition.As a whole, we studied the nanostructures of SiGe driven by its hetero-epitaxial elasticity. We proposed a model to compare two pathways of morphological evolution of SK growth and unearthed the mechanisms of the race and transition. We studied kinetics of island nucleation under the impact of elastic filed produced by an existing island. The peculiar role of strain-dependent surface energy is highlighted. Then the elasticity anisotropy induced by miscut steps on vicinal substrate is studied theoretically and experimentally. This anisotropy effectively induces the elongation of islands in one direction to form nanowires in good alignment. Then the kinetics of condensation of SiGe is studied, which is found to be an effective method in fabricating strained SiGe nanostructures.