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A comprehensive review of the history and present status of ferrite memory materials is presented. The range of topics treated extends from the physical theories dealing with the origin of hysteresis loop squareness and the mechanism of flux switching to the technology of manufacturing memory cores. Themes that underlie the engineering, physics, and chemistry of memory cores are emphasized, particularly in respect to the material requirements for coincident current application. The limitations of memory cores and future prospects for this technology are discussed. Wherever possible an endeavor is made to syncretize, although in a critical and selective way, the sometimes conflicting theories and interpretations of experimental data.