In machine learning, artificial neural networks (ANNs) are becoming indispensable tools, showing impressive results in various applications such as robotics, game development, picture and speech synthesis, and more. Nevertheless, there are inherent disparities between the operational mechanisms of artificial neural networks and the real brain, specifically concerning learning procedures. This chapter covers the overview of Brain-Inspired Computing, its key principles, importance, applications, and future directions. This work also thoroughly examines the learning patterns inspired by the brain in neural network models. We explore the incorporation of biologically realistic processes, including plasticity in synapses, to enhance the potential of these networks. Furthermore, we thoroughly examine this method's possible benefits and difficulties. This review identifies potential areas of investigation for further studies in this fast-progressing discipline, which may lead us to a deeper comprehension of the fundamental nature of intelligence.