Hand, foot, and mouth disease (HFMD) is a common childhood infectious disease caused by various enteroviruses. China has the most significant number of reported cases and deaths of HFMD over the globe. Understanding the epidemic laws of HFMD can provide a scientific basis for designing prevention and control measures. The dynamic transmission models focus on the transmission mechanism of infectious diseases. They can simulate the actual situation to study the epidemic rules of diseases by adding, deleting, and subdividing compartments. More researchers have paid attention to dynamic models because of their high flexibility. To carry out the dynamic model of the HFMD research more effectively, a comprehensive understanding of related research progress in this field is deeply needed. In this paper, based on various researchers' different research purposes of dynamic models, the research progress was classified and summarized, providing meaningful guidance for model construction methods and future research directions and references for dynamic modeling of other models of infectious diseases. It was found that most studies used the SIR dynamic model or its extended model (such as the SEIR model), and few studies contained a complex factor compartment. Some important epidemiological parameters (such as R0) were obtained by studying the HFMD cases in a specific region, simulating different intervention scenarios to evaluate the effect of measures, or revealing the future trend by model prediction. However, there is no dynamic model simultaneously considering age structure, population moving, seasonality and periodicity, and vaccination.