Abstract: This paper present a systematic review of recent research progress and outstanding challenges related to the self-heating effect (SHE) in spin-transfer torque magnetic random-access memory (STT-MRAM) devices. As a leading candidate for next-generation non-volatile memory, STT-MRAM combines high-speed read/write capabilities, ultra-high integration density, low power consumption, and exceptional endurance, making it highly promising for applications in computing-in-memory, neuromorphic computing, and other advanced computing paradigms. However, with the scaling down of device dimensions and the demand for the higher storage density increases, the high current densities required during writing inevitably lead to Joule heating, causing transient local temperature elevations — particularly within the magnetic tunnel junction (MTJ). These rapid thermal fluctuations not only affect the thermal stability of the magnetic layers but also promote the formation of interfacial defects and accelerate material degradation, thereby compromising long-term reliability. Extensive studies have demonstrated that SHE degrades device endurance and markedly increases the write error rate (WER), with underlying mechanisms often exhibiting nonlinear and stochastic behavior. This review synthesizes recent advances in understanding SHE in STT-MRAM, provides an in-depth analysis of its impact on endurance and WER, and outlines key challenges and future research directions, particularly in the context of emerging computing-in-memory architectures.