This review focuses on electrochemical metallization memory cells (ECM), highlighting their advantages as the next generation memories. In a brief introduction, the basic switching mechanism of ECM cells is described and the historical development is sketched. In a second part, the full spectra of materials and material combinations used for memory device prototypes and for dedicated studies are presented. In a third part, the specific thermodynamics and kinetics of nanosized electrochemical cells are described. The overlapping of the space charge layers is found to be most relevant for the cell properties at rest. The major factors determining the functionality of the ECM cells are the electrode reaction and the transport kinetics. Depending on electrode and/or electrolyte material electron transfer, electro-crystallization or slow diffusion under strong electric fields can be rate determining. In the fourth part, the major device characteristics of ECM cells are explained. Emphasis is placed on switching speed, forming and SET/RESET voltage, R(ON) to R(OFF) ratio, endurance and retention, and scaling potentials. In the last part, circuit design aspects of ECM arrays are discussed, including the pros and cons of active and passive arrays. In the case of passive arrays, the fundamental sneak path problem is described and as well as a possible solution by two anti-serial (complementary) interconnected resistive switches per cell. Furthermore, the prospects of ECM with regard to further scalability and the ability for multi-bit data storage are addressed.