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For many decades CMOS devices have been successfully scaled down to achieve higher speed and increased performance of integrated circuits at lower cost. Today’s charge-based CMOS electronics encounters two major challenges: power dissipation and variability. Spintronics is a rapidly evolving research and development field, which offers a potential solution to these issues by introducing novel ‘more than Moore’ devices. Spin-based magnetoresistive random-access memory (MRAM) is already recognized as one of the most promising candidates for future universal memory. Magnetic tunnel junctions, the main elements of MRAM cells, can also be used to build logic-in-memory circuits with non-volatile storage elements on top of CMOS logic circuits, as well as versatile compact on-chip oscillators with low power consumption. We give an overview of CMOS-compatible spintronics applications. First, we present a brief introduction to the physical background considering such effects as magnetoresistance, spin-transfer torque (STT), spin Hall effect, and magnetoelectric effects. We continue with a comprehensive review of the state-of-the-art spintronic devices for memory applications (STT-MRAM, domain wall-motion MRAM, and spin–orbit torque MRAM), oscillators (spin torque oscillators and spin Hall nano-oscillators), logic (logic-in-memory, all-spin logic, and buffered magnetic logic gate grid), sensors, and random number generators. Devices with different types of resistivity switching are analyzed and compared, with their advantages highlighted and challenges revealed. CMOS-compatible spintronic devices are demonstrated beginning with predictive simulations, proceeding to their experimental confirmation and realization, and finalized by the current status of application in modern integrated systems and circuits. We conclude the review with an outlook, where we share our vision on the future applications of the prospective devices in the area. [ABSTRACT FROM AUTHOR]