Grain boundaries influence a wide array of physical properties in polycrystalline materials and play an important role in governing microstructural evolution under extreme environments. While the importance of interfaces is well documented, their properties are among the least understood of all the defect types present in engineering material systems. This is due to the vast configurational space of interfaces, resulting in a diverse range of structures and properties. In the talk, I will present statistical tools (two-point correlation functions and dimensionality reduction techniques) for constructing reliable reduced-order models for energies as a function of the complete crystallographic degrees of freedom of interfaces. These techniques are expected to play an important role in the analysis of grain boundary structure-property relationships as they may be extended to the quantification of complex properties, such as diffusivity, conductivity, corrosion resistance, and defect-interface interactions.