The conventional computing method based on the von Neumann architecture is limited by a series of problems such as high energy consumption, finite data exchange bandwidth between processors and storage media, etc., and it is difficult to achieve higher computing efficiency. A more efficient unconventional computing architecture is urgently needed to overcome these problems. Neuromorphic computing and stochastic computing have been considered to be two competitive candidates for unconventional computing, due to their extraordinary potential for energy-efficient and high-performance computing. Although conventional electronic devices can mimic the topology of the human brain, these require high power consumption and large area. Spintronic devices represented by magnetic tunnel junctions (MTJs) exhibit remarkable high-energy efficiency, non-volatility, and similarity to biological nervous systems, making them one of the promising candidates for unconventional computing. In this work, we review the fundamentals of MTJs as well as the development of MTJ-based neurons, synapses, and probabilistic-bit. In the section on neuromorphic computing, we review a variety of neural networks composed of MTJ-based neurons and synapses, including multilayer perceptrons, convolutional neural networks, recurrent neural networks, and spiking neural networks, which are the closest to the biological neural system. In the section on stochastic computing, we review the applications of MTJ-based p-bits, including Boltzmann machines, Ising machines, and Bayesian networks. Furthermore, the challenges to developing these novel technologies are briefly discussed at the end of each section.

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