We present a review and primer on the subject of conductive bridging random access memory (CBRAM), a metal ion-based resistive switching technology, in the context of current research and the near-term requirements of the electronics industry in ultra-low energy devices and new computing paradigms. We include extensive discussions of the materials involved, the underlying physics and electrochemistry, the critical roles of ion transport and electrode reactions in conducting filament formation and device switching, and the electrical characteristics of the devices. Two general cation material systems are given-a fast ion chacogenide electrolyte and a lower ion mobility oxide ion conductor, and numerical examples are offered to enhance understanding of the operation of devices based on these. The effect of device conditioning on the activation energy for ion transport and consequent switching speed is discussed, as well as the mechanisms involved in the removal of the conducting bridge. The morphology of the filament and how this could be influenced by the solid electrolyte structure is described, and the electrical characteristics of filaments with atomic-scale constrictions are discussed. Consideration is also given to the thermal and mechanical environments within the devices. Finite element and compact modelling illustrations are given and aspects of CBRAM storage elements in memory circuits and arrays are included. Considerable emphasis is placed on the effects of ionizing radiation on CBRAM since this is important in various high reliability applications, and the potential uses of the devices in reconfigurable logic and neuromorphic systems is also discussed.