High-Temperature Gas-Cooled Reactors (HTGRs) have emerged as one of the most promising technologies for sustainable, efficient, and safe system energy generation. Despite their advantages, the thermodynamic performance of HTGRs is often limited by inherent irreversibility, complex thermal-hydraulic interactions, and operational constraints. Exergy analysis has proven to be a powerful tool for identifying, quantifying, and minimizing these inefficiencies, offering critical insights into system design and operational improvement. Alongside this, multi-objective optimization provides a systematic framework to enhance multiple performance indicators simultaneously, enabling engineers to balance competing objectives such as maximizing thermal efficiency, minimizing exergy destruction, reducing operational costs, and improving overall system sustainability. This review focuses on the integration of Multi-Objective Evolutionary Algorithms (MOEAs) with exergy-based analysis for HTGR optimization. Key methodologies, including Pareto-based, indicator-based, and hybrid evolutionary approaches, are examined in detail, highlighting their effectiveness in navigating complex trade-offs and achieving convergence in high-dimensional design spaces. The study synthesizes recent advancements in algorithm development, performance evaluation, and application strategies, emphasizing the potential of MOEAs to significantly improve reactor thermodynamic efficiency while providing robust decision-making tools for reactor designers. Finally, current challenges and future research directions are discussed, including the development of hybrid optimization frameworks, incorporation of uncertainty quantification, real-time operational optimization, and the extension of these methodologies to next-generation reactor systems, aiming to foster sustainable and high-performance energy solutions.