This work focuses on the investigation of overgrowth phenomena in InAs/GaAs nanostructures using synchrotron radiation. Surface-sensitive grazing incidence small angle x-ray scattering (GISAXS) and grazing incidence diffraction (GID) are applied to study shape, strain, and interdiffusion in self-organised grown nanostructures. The technique of anomalous x-ray diffraction at the weak (200) superstructure reflection enhances the chemical sensitivity of the measurements. For the investigation of (partially) buried nanostructures finite-element simulations (FEM) have been performed. The following sample systems were investigated: ((1)) Free-standing and buried InGaAs quantum dots: Free-standing In(x)Ga(1-x)As islands grown on GaAs (001) by molecular beam epitaxy (MBE) with a nominal concentration of x=0.5 have been investigated. Contrast variation close to the K edge of As by anomalous GID at the (200) superstructure reflection is used for a direct determination of the InAs concentration as a function of the lateral strain in the quantum dots (QDs). The evaluation of intensity mappings recorded in reciprocal space close to the (200) reflection together with atomic force micrographs (AFM) allows to attribute the strain and the InAs concentration to a certain height in the quantum dots. Thereby, a three-dimensional model of the strain and interdiffusion profile of the InGaAs QDs can be reconstructed. A discussion of measurements taken on buried InGaAs QDs and free-standing islands grown on the strain modulated surface of a buried QD layer shows the limits of this technique. ((2)) InGaAs quantum rings: The formation of nanoscopic InGaAs ring structures on a GaAs (001) substrate takes place when InAs quantum dots, grown by Stranski-Krastanov self-organisation, are covered by a thin layer of GaAs. The shape transformation into rings is governed by strain, diffusion and surface tension, quantities which are of importance to understand magneto-optical and electronic applications of the rings. GISAXS and GID is applied to characterise morphology and structural properties such as strain and chemical composition of the rings in three dimensions. From GISAXS the shape is found to be of circular symmetry with an outer radius of 26nm, a height of 1.5nm, and a hole in the middle, in good agreement with AFM measurements. The most surprising results are obtained from intensity mappings in reciprocal space close to the (220) and (2-20) reflection done in surface sensitive GID geometry. From a comparison of the intensity maps with FEM model calculations the InGaAs interdiffusion profile in the ring is determined. It strongly depends on the crystallographic orientation. In the ring a maximum InAs concentration of more than 80% along [1-10] is found while along [110] it is below 20%. This is explained by the preferred diffusion of In along [1-10]. ((3)) Quantum wires formed by cleaved edge overgrowth: Quantum wires (QWRs) fabricated by the cleaved edge overgrowth (CEO) technique use tensile strain to confine the charge carriers to one dimension. The cleaved edge of a pseudomorphically strained In0.1Al0.9As/Al0.33Ga0.67As superlattice (SL) is overgrown by a GaAs layer of 10nm thickness. The lateral charge carrier localisation in the overgrown layer is induced by the periodic strain modulation of the SL. Using GID this strain state of the system is determined. The strain modulation due to the overgrown superlattice occurs only within 3micron of the total wafer thickness of 150micron. The GID technique allows for a clear separation of the strain modulation in the cap layer and the superlattice underneath. It can be proved that the strain modulation in the GaAs cap layer is not of compositional origin but purely elastic with an average lattice parameter change of (0.8+-0.1)% with respect to relaxed GaAs. The strain profile obtained is confirmed by