The investigation of plutonium in glasses (amorphous ceramics lacking long-range order), in crystalline ceramics, and in composite materials composed of multiple crystalline or glass and crystalline phases, relieson multidisciplinary studies of physics, chemistry, and materials science. It involves the study of the plutonium atoms in materials with only short-range periodicity, as in glasses, to materials with long-range periodicity, as in crystals. The materials studied over the past 30 years include simple binary crystals, used to investigate the electronic structure of plutonium, to complex glasses and ceramics selected not only for the safety and durability that they provide for the immobilization of nuclear waste and plutonium, but also for the high flexibility they offer in composition. The lack of long-range order at the atomic level in glasses permits the inclusion of abroad range of waste elements, but it renders more difficult the interpretation of data from many commonly used experimental techniques. Regardless of the challenge, much of the research conducted in this field over the past few decades has been motivated by the use of plutonium as a surrogate for all nuclear-waste actinides or on its own in immobilization studies, in order to develop a durable glass or ceramic matrix that can resist leaching and mobilization of the plutonium on a geologic time scale.