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Artificial neural networks (ANNs) have emerged as an essential tool in machine learning, achieving remarkable success across diverse domains, including image and speech generation, game playing, and robotics. However, there exist fundamental differences between ANNs’ operating mechanisms and those of the biological brain, particularly concerning learning processes. This paper presents a comprehensive review of current brain-inspired learning representations in artificial neural networks. We investigate the integration of more biologically plausible mechanisms, such as synaptic plasticity, to improve these networks’ capabilities. Moreover, we delve into the potential advantages and challenges accompanying this approach. In this review, we pinpoint promising avenues for future research in this rapidly advancing field, which could bring us closer to understanding the essence of intelligence.