The high density and high speed nonvolatile MTJ MRAMs are reviewed from perspective of the reading and writing operation. The reading operation of the MRAM with different sensing schemes and cell array structures is discussed, in particular the reference resistance generating schemes which are introduced to maximize the cell efficiency and reading reliability. The high density, low cost cross-point cell layout structures are analyzed systematically. The writing operation modes ranging from the half-select, toggle mode, guided SAF direct writing, thermally assisted writing, to the spin transfer switching are investigated both theoretically and experimentally. The thermal factor always plays an important role in determine not only the thermal stability but also the reading and writing reliability.