The Discrete Element Method (DEM) is an innovative numerical computational approach. This method is employed to study and resolve the motion patterns of particles within discrete systems, contact mechanics properties, mechanisms of separation processes, and the relationships between contact forces and energy. Agricultural machinery involves the interactions between machinery and soil, crops, and other systems. Designing agricultural machinery can be equivalent to solving problems in discrete systems. The DEM has been widely applied in research on agricultural machinery design and mechanized harvesting of crops. It has also provided an important theoretical research approach for the design and selection of operating parameters, as well as the structural optimization of potato harvesting machinery. This review first analyzes and summarizes the current global potato industry situation, planting scale, and yield. Subsequently, it analyzes the challenges facing the development of the potato industry. The results show that breeding is the key to improving potato varieties, harvesting is the main stage where potato damage occurs, and reprocessing is the main process associated with potato waste. Second, an overview of the basic principles of DEM, contact models, and mechanical parameters is provided, along with an introduction to the simulation process using the EDEM software. Third, the application of the DEM to mechanized digging, transportation, collection, and separation of potatoes from the soil is reviewed. The accuracy of constructing potato and soil particle models and the rationality of the contact model selection are found to be the main factors affecting the results of discrete element simulations. Finally, the challenges of using the DEM for research on potato harvesting machinery are presented, and a summary and outlook for the future development of the DEM are provided.