With the rise of the low-altitude economy, the application scenarios of unmanned aerial vehicle (UAV) continue to expand, particularly playing a significant role in emergency response. Leveraging advantages such as high mobility and remote control, UAV has proven to be powerful tools in disaster monitoring, communication restoration, personnel search and rescue, material delivery, and post-disaster assessment during emergencies such as natural and human-made disasters. This paper aims to provoide a comprehensive review of modeling methods and the latest research progress in UAV path planning for emergency rescue, offering thorough theoretical references and technical guidance for researchers in related fields. It begins by outlining typical emergency rescue scenarios such as earthquakes, fires, and floods, summarizing the application requirements of UAV in different contexts. Then it systematically reviews UAV path planning modeling methods, including dynamic models and task models, with task models further categorized into hierarchical, collaborative, fault-tolerant, real-time, and adaptative dimensions. Subsequently, it comprehensively analyzes path planning optimization algorithms based on three core elements: constraints, optimization objectives, and solution algorithms. Finally, the paper discusses the challenges and opportunities of UAV path planning in emergency rescue, highlighting that technological development, multi-UAV collaboration, and interdisciplinary integration represent future development opportunities. This study provides theoretical support and practical reference for the further development and application of UAV path planning modeling.