Liquid metal batteries (LMBs) represent a promising solution for grid-scale energy storage compared to other battery technologies, due to their low cost, high power density, excellent cyclability, long cycle life, self-healing characteristics, high Coulombic efficiency, and ease of scalability. The operation of an LMB involves multiple physical processes, including electrochemical reactions, mass transfer, heat transfer, fluid flow, etc. These processes are highly coupled and influence each other significantly, resulting in complex and nonlinear system behavior. As a result, accurately modeling and predicting the performance of LMBs under various operating conditions remains a significant challenge. This review highlights recent advances in LMB modeling and state estimation, providing a critical evaluation of existing frameworks in terms of modeling accuracy, computational efficiency, and practical limitations. It concludes by identifying key challenges and recommending future research directions to improve the reliability and practical deployment of LMBs in large-scale renewable energy systems.This paper is an outcome of a larger program (Stor Cortex) to develop intelligent solutions for storage technologies for the ENOWA.NEOM energy systems and was funded by ENOWA.NEOM through a technical consulting services agreement with KAUST. AMBRI INC (USA) provided the LMB cells and the system on rent to ENOWA.NEOM as part of its LDES Pilot Program Evaluation and under a consulting agreement ‘Ambri's Liquid Metal Battery Demo System’, contract number 1110000033
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