We provide an overview of the field of rigidity theory applied at the atomic scale. This theoretical approach, initially designed for macroscopic structures such as bridges or buildings, has gained renewed interest in the past few years thanks to new methodological developments and to attractive applications in a variety of materials, such as scratch-resistant glassy sheets for mobile phones, phase-change memory, tough cement, dielectrics, and photonic devices. In parallel, basic phenomena associated with the onset of rigidity have been discovered, which have challenged our current understanding of the structural modification induced by changes in composition. This has led to the identification of “smart” glasses with multiple functionalities and superior mechanical performances. Topological prediction and engineering of physical properties are also enabling intelligent design of new disordered materials.
