Characterization of interface structure involves describing and determining the manner in which misfit is distributed. Theories based on crystallography and elasticity are used to discover both minimum misfit lattice misorientations and interface planes. With the crystallographic variables defined the Frankvan der Merwe analysis seeks to determine how the misfit is distributed. Computer modelling embodies an explicitly atomistic approach and has provided a bridge between experiment and other analytical methods. Observations validate many of the theoretical concepts. The facetted TiMn parent martensite interface can be understood in terms of Burger's vector density minimization as can the orientation relationships found between b.c.c. deposits and single-crystal f.c.c. substrates. High resolution transmission electron microscopy confirms the extension of the dislocation wall model for low angle boundaries to rotation angles as high as 26°, which had been suggested by computer modelling. We know that the dislocation structure of an interface does not necessarily lead to a complete understanding of the interface core structure because of complications resulting from relative lattice translations and other sources of multiplicity of structure which are evidenced through observations of imperfect interface dislocations and directly through measurement of not necessarily crystallographically equivalent lattice translations. In simple cases high resolution transmission microscopy, ion channelling and UV photoelectron spectroscopy sometimes in combination have permitted a full determination of the atomic structure of interfaces and revealed the physical nature and reality of low energy dislocation structures. © 1987.