With the advent of the Big Data era, neuromorphic computing (NC) (also known as brain‐inspired computing) has gained a lot of research interest. Spintronic devices are the emerging candidates for implementing the NC due to their intrinsic nonvolatility, extremely high endurance, low‐power consumption, and complementary metal‐oxide compatibility. Many research groups have proposed various NC architectures based on spintronic devices. Herein, a collective survey of different spintronic‐based approaches is given for NC. The reviewed approaches include the progress of stochastic magnetic tunnel junction (MTJ) devices, spin‐torque nano‐oscillator, spin‐Hall nano‐oscillator, domain walls, and skyrmion devices. In all of these approaches, spin–orbit torque (SOT)‐based magnetization control, which is achieved via spintronics heterostructures, plays a significant role. Various heterostructures of heavy metal and ferromagnetic layers that have been proposed are reviewed for generating SOT. In addition, the phenomena and materials involved in the generation of orbital torque are summarized due to the orbital Hall effect (OHE), which has recently gained researchers’ attention. Finally, an outlook on the opportunities and challenges for spintronic‐based NC hardware is provided, shedding light on its great potential for artificial intelligence (AI) applications.