Heavy-duty industrial robots are increasingly utilized in machining applications due to their advantages such as large workspace and flexible posture. However, their inherent stiffness characteristics render them highly susceptible to chatter during machining operations, significantly constraining their application and development. Research on chatter prediction based on high-precision dynamic modeling, along with various active and passive chatter suppression techniques, is crucial for achieving chatter-free machining. This paper systematically reviews the research progress in the dynamics of heavy-duty robotic machining systems globally. Firstly, the methods for modeling and predicting the dynamic characteristics of heavy-duty robots are introduced. Subsequently, an in-depth analysis of the dynamics model of the milling process and its solution methods is provided, elucidating the mechanisms of chatter, influencing factors, and variations in dynamic behavior. Furthermore, online chatter monitoring techniques and comprehensive suppression strategies are presented, evaluating the characteristics, applicable scenarios, advantages, and limitations of different approaches. Finally, based on the above analysis, a summary is provided along with key directions for future research. Through a comprehensive review and in-depth discussion of the dynamics research in heavy-duty robotic machining, this work aims to serve as a valuable reference and provide directional guidance for scholars in related fields.