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Permanent magnet motors (PMMs) have emerged as key components in numerous industrial applications due to their high efficiency, compact size, and robust performance characteristics. However, to attain optimal performance in PMM drives, accurately predicting and mitigating core losses is paramount. This paper aims to provide a comprehensive review of advancements and methodologies for enhancing the performance of PMM drives by integrating equivalent circuit models (ECMs) that account for core losses. Firstly, the significance of core losses in motor drives is underscored, alongside a survey of research endeavors dedicated to core loss reduction. Notably, emphasis is placed on mathematical models offering both swift computation and reasonable accuracy. Subsequently, the paper delves into the development of ECMs, focusing on approaches adept at capturing core loss effects across diverse operating conditions. Moreover, this paper explores the utilization of these improved ECMs in the design and control of PMMs to achieve enhanced performance. By integrating core loss considerations into design and control strategies, PMM drives can optimize efficiency, torque production, and overall system performance. In summary, this paper may consolidate the current state-of-the-art techniques for enhancing PMM performance through the integration of core-loss-aware ECMs. It highlights key research directions and opportunities for further advancements in this critical area, aiming to foster the development of more efficient and reliable PMM-based systems for a wide range of industrial applications. [ABSTRACT FROM AUTHOR]