Many metal-insulator-metal systems show electrically induced resistive switching effects and have therefore been proposed as the basis for future non-volatile memories. They combine the advantages of Flash and DRAM ( dynamic random access memories) while avoiding their drawbacks, and they might be highly scalable. Here we propose a coarse-grained classification into primarily thermal, electrical or ion-migration-induced switching mechanisms. The ion-migration effects are coupled to redox processes which cause the change in resistance. They are subdivided into cation-migration cells, based on the electrochemical growth and dissolution of metallic filaments, and anion-migration cells, typically realized with transition metal oxides as the insulator, in which electronically conducting paths of sub-oxides are formed and removed by local redox processes. From this insight, we take a brief look into molecular switching systems. Finally, we discuss chip architecture and scaling issues.