Mullite (3Al2O3.2SiO2) is becoming increasingly important in electronic, optical, and high-temperature structural applications. This paper reviews the current state of mullite-related research at a fundamental level, within the framework of phase equilibria, crystal structure, synthesis, processing, and properties. Phase equilibria are discussed in terms of the problems associated with the nucleation kinetics of mullite and the large variations observed in the solid-solution range. The incongruent melting behavior of mullite is now widely accepted. Large variations in the solid solubility from 58 to 76 mol% alumina are related to the ordering/disordering of oxygen vacancies and are strongly coupled with the method of synthesis used to form mullite. Similarly, reaction sequences which lead to the formation of mullite upon heating depend on the spatial scale at which the components are mixed. Mixing at the atomic level is useful for low-temperature (< 1000-degrees-C) synthesis of mullite but not for low-temperature sintering. In contrast, precursors that are segregated are better suited for low-temperature (1250-degrees to 1500-degrees-C) densification through viscous deformation. Flexural strength and creep resistance at elevated temperatures are significantly affected by the presence of glassy boundary inclusions; in the absence of glassy inclusions, polycrystalline mullite retains > 90% of its room-temperature strength to 1500-degrees-C and displays very high creep resistance. Because of its low dielectric constant, mullite has now emerged as a substrate material in high-performance packaging applications. Interest in optical applications mainly centers on its applicability as a window material within the mid-infrared range.