The Si1-xGex/Si growth usually proceeds by a layer by layer growth of the first monolayers followed by 3D growth of islands on the top of the uniform layer (Stranski-Krastanov mode). Self-organisation of these islands is very attractive to create large arrays of nanoscale structures. This paper deals with the self-organisation of Si1-xGex nanostructures by way of kinetic and thermodynamic manipulations. Solid source-molecular beam epitaxy (SS-MBE) and gas source-MBE (GS-MBE) grown heterostructures are characterised by atomic force microscopy (AFM) and grazing incidence X-ray diffraction (GIXRD). The results concentrate on the role of the atomic configuration of substrates on the metastable shape of islands. By comparing the Si1-xGex layers grown on (111), (001) and misoriented substrates, we prove that the different Si1-xGex morphologies obtained can he explained by different mechanisms of step redistribution on the two nominal orientations. Misoriented surfaces from (111) and from (001) lead to step-bunching roughening and to anisotropic undulations perpendicular to the atomic steps, respectively. The influence of concentration (stress), thickness and annealing on the island-shaped transition is evidenced. Qualitatively, these three parameters induce the same shape evolution: after the onset of "hut" islands, first the island density increases, then a shape transition going through a bimodal distribution of island sizes is observed which leads to the complete transformation into "dome"-shaped islands in the end. The results show that whatever is the underlying mechanism, the onset of the shape transition is related to a critical aspect ratio (h/L) of the islands and to typical level of stress relaxation as shown by GIXRD analysis.