Examples of applications of x-ray scattering techniques to the characterization of Si/Si1-xGex heterostructures on (001) Si grown by either molecular beam epitaxy (MBE) or ultrahigh vacuum chemical vapor deposition (UHV-CVD) are presented. Triple-axis high-resolution x-ray diffraction is used to investigate morphological instabilities in Si/Si1-xGex multilayers grown at high temperature. Intensity mapping of highly asymmetric Bragg reflections reveals the presence of undulations along [100] directions. The amplitude and wavelength of the undulations can be adjusted by appropriate choice of growth conditions and structure geometry, which offers interesting prospects for the design of Si1-xGex quantum wires and dots. Specular reflectivity and diffuse scattering is used to estimate the interface roughness and its characteristic length scale and correlation of Si/Si1-xGex heterostructures. Interfaces in superlattices are generally narrow (0.3-0.5 nm), highly correlated vertically, and influenced by growth conditions. Heterostructures grown by MBE or UHV-CVD have comparable interface widths, but structures grown by MBE have a longer autocorrelation length (0.5 mu m versus 30 nm). Diffraction and grazing angle specular reflectivity is also used to study diffusion processes in Si/Si1-xGex heterostructures upon thermal annealing. The analysis reveals an enhancement of the diffusion in the early stage of annealing that is not due to strain, but may be linked to grown-in, nonequilibrium point defects. The large difference in the diffusivity of Ge in Si and Ge also causes an anisotropy in the diffusion, which leads to the broadening of Si1-xGex quantum wells upon annealing.