Multi-layer semiconductor structures (quantum wells and grain boundaries) grown by molecular beam epitaxy (MBE) as well as precipitates in glasses are investigated by high resolution electron microscopy (HREM) providing local atomic information at the relaxed interfaces. The interpretation of the micrographs requires methods of image analysis and the computer simulation of the HREM contrast by calculating the electron beam specimen interaction of a theoretical structure model, and by subsequently considering the electron-optical process. The relaxed atomic structures of the interfaces are modelled by molecular dynamics and energy minimization with the bonding forces and the parameters of the pair and three-body potentials being varied. Possibilites will be discussed of revealing the compositional variations and the elastic deformations at the interfaces by HREM imaging under special imaging conditions.