Mullite has achieved outstanding importance as a material for both traditional and advanced ceramics because of its favourable thermal andmechanical properties. Mullite displays various Al to Si ratios referring to the solid solution Al4+2xSi2−2xO10−x, with x ranging between about 0.2and 0.9 (about 55 to 90 mol% Al2O3). Depending on the synthesis temperature and atmosphere mullite is able to incorporate a number of transitionmetal cations and other foreign atoms. The crystal structure of mullite is closely related to that of sillimanite, which is characterized by chainsof edge-connected AlO6 octahedra running parallel to the crystallographic c-axis. These very stiff chains are cross-linked by tetrahedral chainsconsisting of (Al,Si)O4 tetrahedra. In more detail: Parallel to a the tetrahedra are linked to the relatively short more stiff Al–O(A, B) bonds, whereasparallel b they are linked parallel to the relatively long more compliant Al–O(D) bonds. In mullite some of the oxygen atoms bridging the tetrahedraare removed for charge compensation. This gives rise to the formation of oxygen vacancies and of T3O groups (so-called tetrahedral triclusters).The anisotropy of the bonding system of mullite has a major influence on the anisotropy of its physical properties. For example:• the highest longitudinal elastic stiffness is observed parallel c, but lower ones parallel a and especially parallel b,• the maximum of the thermal conductivity occurs parallel c, but maller ones parallel a and especially parallel b,• large thermal expansion especially parallel b,• fastest crystal growth and highest corrosion parallel c.Heat capacity and thermal expansion measurements of mullite display reversible anomalies in the temperature range between about 1000 and1200 ◦C. It is believed that tetrahedral cations, bridging O atoms, and O vacancies undergo dynamical site exchange processes at high temperatures.At lower temperatures the dynamic disorder may transform to a static one. Diffraction experiments revealed that also partially ordered states mayexist.