Memory effects in complex materials and nanoscale systems

Memory effects are ubiquitous in nature and are particularly relevant at the nanoscale where the dynamical properties of electrons and ions strongly depend on the history of the system, at least within certain time scales. We review here the memory properties of various materials and systems which appear most strikingly in their non-trivial time-dependent resistive, capacitative and inductive characteristics. We describe these characteristics within the framework of memristors, memcapacitors and meminductors, namely memory circuit elements whose properties depend on the history and state of the system. We examine basic issues related to such systems and critically report on both theoretical and experimental progress in understanding their functionalities. We also discuss possible applications of memory effects in various areas of science and technology ranging from digital to analog electronics, biologically-inspired circuits, and learning. We finally discuss future research opportunities in the field.