Abstract: The atomic-scale structure of tilt grain boundaries has been studied by high-resolution electron microscopy (HREM) in several ceramics and metals such as NiO, yttria stabilized zirconia, Au, and Al. It is found that when grain boundaries are formed between two crystals a considerable variety of modes of relaxations, i.e., the rearrangements of atoms in and near the grain boundary core are possible, depending on grain boundary geometry and the interatomic interactions. The atomic relaxations within and near the grain boundary core often include relaxations that involve the formation of stacking faults in low-stacking-fault energy fcc materials. Grain boundary dissociations are also observed for several grain boundary geometries. Computer simulations of grain boundary structures in metals have in general been able to reproduce the relaxation features at least on a qualitative level. In contrast, ceramic grain boundaries typically are more complex and not always tractable by simple computer relaxation procedures, since the formation of point defects and partial occupancy of atomic columns may be involved in the relaxation processes. It is found that when a boundary is not allowed to relax to its lowest energy state due to geometrical constraints, a multitude of grain boundary core structures can exist. Such conditions are expected to be characteristic for nanocrystalline materials. Because of its close connection to grain boundary properties, quantification of the volume expansion by HREM techniques is an important goal of grain boundary research. Image simulations of grain boundaries suggest that for most materials of interest the 3-fold astigmatism must be corrected to better than 100 nm to achieve the desired accuracies.