The dihedral angle is the angle subtended between two grain boundaries at a three-grain junction, or the angle between the two liquid-solid interfaces at the corner of a fluid-filled pore. In textural equilibrium the dihedral angle defines the topology, interconnectivity and amount of a liquid phase. Complete textural equilibrium (in terms of uniform grain size, constant mean curvature of grain boundaries and balancing of interfacial energies at all three- and four-grain junctions) is rare in geological materials, particularly in the crust. Local equilibrium at grain junctions (manifest as dihedral angles) is generally seen in monomineralic rocks, in high-grade metamorphic rocks and in the mantle. The distribution of true dihedral angles, as measured using a universal stage, has great potential use in interpretation of rock history. The studies of disequilibrium dihedral angles are currently at the descriptive stage, and further efforts need to be applied to deriving a quantitative understanding of the processes by which, and rates at which, they attain equilibrium.