Internal interfaces (II) play an important, sometimes controlling, role, for many properties of polycrystalline materials. Direct information on the structure of II can be retrieved from High-Resolution Transmission Electron Microscopy (HRTEM) studies. From one HRTEM micrograph information on the projection of the structure parallel to the direction of the incoming electron beam can be obtained, if the electron beam is parallel to low ordered Laue zones in both crystals adjacent to the II. Three-dimensional information on the structure requires studies for different directions of the incoming beam (tomographic studies). The reliability (accuracy) of the investigations depends on (i) the nature and quality of the specimen and (ii) on the resolution power of the TEM. Corrector elements for major aberrations of the TEM lenses resulted in major improvements of the resolution of the instruments. The resolution limit lies in state-of-the-art instruments below 0.1 nm.

In this lecture a short introduction to the possibilities and limitations of quantitative HRTEM of interfaces will be given, followed by the presentation of results for grain boundaries (gb) in artificially processed bicrystals of metals and ceramics. The gb structure can be determined with high precision and the results will be compared to results of computer simulations of the identical gb. Investigations of "general" gbs (experimentally and theoretically) are much more complicated. Pathways for the studies will be presented. Heterophase boundaries, e.g., metal/ceramic interfaces, were also analysed. Some representative results will be shown and discussed. Difficulties and problems concerning the TEM specimen are laid out. Progress in the field depends very strongly on the availability of TEM specimens suitable for the investigations.