Abstract: Magnetic random access memory（MRAM） is a novel information storage device based on spintronics. Its building block typically consists of a magnetic tunnel junction, which is a sandwich structure with two ferromagnetic layer and one insulating barrier. The relative directions of the ferromagnets’ magnetizations lead to high and low resistance states, which is then employed to store the data in a non-volatile fashion. MRAM has extremely fast switching speed, nearly zero leakage power consumption and extremely high reliability, all of which stands it out as one of the ideal devices for in-memory computing applications. This review discusses the research progresses on MRAM based in-memory computing, including the basic device structures and corresponding control methods. We will then mainly focus on the description of current status of MRAM based in-memory computing using arithmetic logic and neural network. Finally, some challenges and perspectives on the field are given.