Nonvolatile spintronic devices have potential advantages, such as fast read/write and high endurance together with back-end-of-the-line compatibility, which offers the possibility of constructing not only stand-alone RAMs and embedded RAMs that can be used in conventional VLSI circuits and systems but also standby-power-free high-performance nonvolatile CMOS logic employing logic-in-memory architecture. The advantages of employing spintronic devices, especially magnetic tunnel junction (MTJ) devices with CMOS circuits, are discussed, and the current status of the MTJ-based VLSI computing paradigm is presented along with its prospects and remaining challenges.