Abstract: Under the background of "double carbon", the large-scale integration of new energy sources into the power grid necessitates coal-fired power units to undertake peak-shaving tasks, resulting in prolonged transient operation. The flexibility of their operations needs further enhancement. However, deep peak-shaving and rapid load changes reduce the operational reliability of these units, with their flexible peak-shaving capability being constrained by equipment safety concerns. This paper reviews the current state of research on the safe and stable operation of coal-fired power units under flexible peak-shaving conditions. First, it summarizes the safety technical issues associated with the heat exchange surfaces of boilers and turbine rotors under peak-shaving operating conditions, elucidating the impact of flexible operation on the safety of unit equipment. Next, it provides a comparative analysis of the advantages, disadvantages, and applicability of various methods for monitoring key operating parameters such as temperature and stress. Finally, the paper discusses existing methods for optimizing operational parameters and equipment structures to address identified safety technical issues. Finally, the current research summarizes the current research status and challenges of the flexible and safe operation of coal-fired power units and provides an outlook on future research directions.