Demand for new computing systems equipped with ultra-high-density memory storage and new computer architecture is rapidly increasing with the tremendous increment of the amount of data produced and/or reproduced. In particular, the requirement for technology development is growing as conventional storage devices face the physical limitations for scaling down and the data bottleneck that the Von Neumann architecture increases. Among the recent emerging memory devices, the conductive bridge random access memory (CBRAM) has superior switching properties and excellent scalability to be adopted as the next-generation storage device and as the hardware implementation of the neuromorphic computing system. In this review, the previous papers on the resistive switching mechanism of CBRAM and the precedent CBRAM devices exploiting various materials proposed by many research groups are introduced. The principle of CBRAM is discussed including the operation mechanism, switching materials, and the challenges that need to be solved. A wide selection of materials including metal oxides, Chalcogenides, and other non-oxides have been examined as the electrolyte layer of the CBRAM. Various switching materials, device engineering, and material innovation approaches were introduced, and the research results for solving the problems of CBRAM were reviewed in depth.