Magnetoresistive random access memory (MRAM) is a promising non-volatile memory technology that can be utilized as an energy and space-efficient storage and computing solution, particularly in cache functions within circuits. Although MRAM has achieved mass production, its manufacturing process still remains challenging, resulting in only a few semiconductor companies dominating its production. In this review, we delve into the materials, processes, and devices used in MRAM, focusing on both the widely adopted spin transfer torque MRAM and the next-generation spin-orbit torque MRAM. We provide an overview of their operational mechanisms and manufacturing technologies. Furthermore, we outline the major hurdles faced in MRAM manufacturing and propose potential solutions in detail. Then, the applications of MRAM in artificial intelligent hardware are introduced. Finally, we present an outlook on the future development and applications of MRAM.