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This paper provides an in-depth review of the magnetoresistive random access memory technology and its developments over the past decade. Both the traditional field-driven and more recent spin torque transfer driven designs are discussed. By pointing out key technical challenges, important aspects and characteristics of various designs are used to illustrate mechanisms that overcome the technical obstacles. A significant portion of this paper is devoted to the principles of various designs based on spin torque transfer effect, including memory elements with in-plane and perpendicular magnetic electrodes.