Currently, urban rail transit is facing the challenges of relatively high energy consumption as well as relatively low passenger service levels. Optimizing train operations is crucial for achieving energy savings, enhancing service quality, and ensuring safety. This paper reviews research progress on optimization based on passenger flow and energy-saving objectives. In terms of passenger flow, existing studies are categorized into four areas: timetable design, transport organization, coordinated control, and real-time optimization. However, limitations remain in handling unexpected passenger surges, multi-mode coordination, and algorithmic reliability. Regarding energy efficiency studies are summarized at three levels: integration with passenger flow, single-train control, and multi-train coordination. Challenges include real-time performance of models, coordination across different control levels, and robustness of solutions. Future research should focus on integrated full-link optimization, stronger robustness, and improved applicability in engineering practice.