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Fossil fuel usage has a great impact on the environment and global climate. Promoting new energy vehicles (NEVs) is essential for green and low-carbon transportation and supporting sustainable development. Lithium-ion power batteries (LIPBs) are crucial energy-storage components in NEVs, directly influencing their performance and safety. Therefore, exploring LIPB reliability technologies has become a vital research area. This paper aims to comprehensively summarize the progress in LIPB reliability research. First, we analyze existing reliability studies on LIPB components and common estimation methods. Second, we review the state-estimation methods used for accurate battery monitoring. Third, we summarize the commonly used optimization methods in fault diagnosis and lifetime prediction. Fourth, we conduct a bibliometric analysis. Finally, we identify potential challenges for future LIPB research. Through our literature review, we find that: (1) model-based and data-driven approaches are currently more commonly used in state-estimation methods; (2) neural networks and deep learning are the most prevalent methods in fault diagnosis and lifetime prediction; (3) bibliometric analysis indicates a high interest in LIPB reliability technology in China compared to other countries; (4) this research needs further development in overall system reliability, research on real-world usage scenarios, and advanced simulation and modeling techniques. [ABSTRACT FROM AUTHOR]