It has been shown that the concepts used to determine the equilibrium shape of crystals can be extended to determine the conditions under which grain boundaries will be fully wetted, partially wetted, or not wetted by a second phase. Recent experimental observations on the equilibrated morphologies of solid or fluid wetting phases along grain boundaries, reveal features that are predicted, and in some cases required, by this construction. Theory distinguishes between cases where surfaces are smoothly curved or where there are facets, edges and corners. In the latter case the conventional comparison of the energy of the original grain boundary with the sum of the surface energy of the two surfaces of the wetting layer leads to erroneous predictions. The correct predictions are obtained by comparing the Wulff shape of the grain boundary (the interfacial energy minimizing shape for a fixed volume of material) with a carefully defined sum of Wulff shapes of the surfaces of the wetting layer. Where orientations that are wetted join with those that are not, there is almost always an abrupt change of orientation. Faceting on two hierarchical levels can occur. Microscopic morphology changes along macroscopically curved surfaces follow well defined rules predicted by theory. The analogy between the thermodynamics of interface faceting and phase transformations allows the well known concepts of phase equilibria to be used to understand the predicted structures. The predictions of the model will be used to identify the nature of the faceting observed in alumina in the presence of a second phase.