This article identifies singular interfaces according to singularity in terms of structural defects, including dislocations and ledges. Defect singularities are defined by the elimination of one or more classes of defects, which must be present in the vicinal interfaces. In addition to the three commonly classified structural interfaces, a new type of interface-the CS-coherent interface-is introduced. Singularities in dislocation and ledge structures have been integrated in the study of orientation relationships (OR). The dislocation structures are determined through the O-lattice theory, originally proposed by Bollmann. The basic concepts of the O-lattice and related formulas from the original theory and extended studies are briefly reviewed. According to the theory, singular interfaces exhibiting singularity in the dislocation structures have been identified. An interface that is singular with respect to the interface orientation must be normal to at least one Delta g, a vector connecting two reciprocal points from different lattices. An interface that is singular also with respect to the OR must obey one or more Delta g parallelism rules. The selection of proper Delta gs for different preferred states of interfaces are explained. Identification of singular interfaces with measurable Delta gs provides a convenient and effective approach to the interpretation of the observed facets and ORs. The ambiguity about the selection of the deformation matrix (A) for the O-lattice calculation and the advantage of the O-lattice approach over the approach using the Frank-Bilby equation for the calculation of the interfacial dislocations are clarified. Limitations of the present approach and further study are discussed.