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Phase-change materials exhibit some remarkable properties which have, over the last four decades, led to the successful development of both optical and electrical binary phasechange memories. However, as pointed out by the ‘father of phase-change materials’ himself, Stanford R. Ovshinsky, such binary memories only ‘scratch the surface’ in terms the extraordinary functionality that phase-change systems offer. This functionality extends to non-binary arithmetic processing, non-volatile logic, neuronal/synaptic mimics and cognitive computing — all available in both the electrical and optical domains, or indeed using a mixture of the two. Here Wright et al. (pp. 1978–1984) introduce and explain the physical origins of some of this remarkable functionality and outline some exciting potential applications for phase-change materials and devices, beyond the confines of simple binary memories. The authors explore the memristive properties of phase-change devices, drawing on an analogy between crystallization behaviour in phase-change cells and the wellknown moving conductive-front memristor model. Exploiting the dual optical—electrical activity of phase-change materials, a new type of device is also described, the memory-refl ector or ‘memfl ector’. Finally, the authors show how a simple phase-change cell can perform arithmetic, including addition, subtraction, multiplication and division, all in high-order bases and with simultaneous storage of the result.