<p>The rapid integration of renewable energy sources and the decentralization of power systems have positioned microgrids as essential for sustainable, resilient energy supply. However, their diverse operating conditions and complex topologies pose challenges for stability, protection, and autonomous control, particularly under fault conditions. This article surveys brain-inspired artificial intelligence (BIAI) models that enable self-healing functions in Microgrids (MGs). It covers structure-driven models, including convolutional, recurrent, and spiking neural networks, alongside behavior-driven approaches such as learning systems (reinforcement, transfer, attention mechanisms, and emotions). A special emphasis is placed on Brain Emotional Learning and its variation, BELBIC, which replicates emotion-driven neural mechanisms to provide adaptive, quick, and less complexity control suited to the nonlinear nature and uncertain behavior of MGs. Evidence reported in the literature suggests that BIAI approaches can improve fault detection, enhance restoration decisions, and support more resilient and adaptive self-healing strategies compared with conventional AI techniques. This review aims to assist researchers and practitioners in developing more robust, adaptive, autonomous self-healing MG architectures. It concludes by highlighting the open challenges and potential future research objectives to accelerate the adoption of BIAI in a dynamic energy environment.</p>