Thermokarst lakes are a major heat source for the adjacent permafrost and a significant source of atmospheric methane. These lakes have important impacts on the physical,chemical,biological,geomorphological and hydrological processes occurring in the ground under and around thermokarst lakes,and seriously affect the local environment and the stability of the structures constructed in permafrost regions. Numerical simulation methods provide an effective method for quantitative analysis of the long-term impact of thermokarst lakes and their evolution on permafrost surrounding the lakes,and have deepened our knowledge about the impact of thermokarst lakes immensely. Summarizing the research progresses in numerical simulation of long-term impact of thermokarst lakes on thermal regime of surrounding permafrost has an important guiding function to improve mathematical models and develop more effective models. In this study,the components,functions,advantages and defects of several typical mathematical models having developed over the past ten years or so were reviewed,such as the heat conduction model with phase change,thaw slumping model,the coupled lake-permafrost model,thaw lake expansion model combining thermal processes with mass wasting and thaw-driven subsidence,the coupled heat conduction and moisture migration model,and the moving mesh method based thermokarst lake dynamic evolution model. Several issues deserving to be paid further attention in the future researches were proposed,including creating more effective models, determining the more realistic initial condition,lucubrating thermal and physical parameters of the typical soils,consider the impact of lake water replenishment,quantitative analysis of the thermal effect of supra-permafrost water flow around the thermokarst lakes,creating the coupled governing equation of heat conduction with phase change and convective heat transfer,embed ding the effect of climate warming in the model,numerical investigation of the long-term influence of thermokarst lake drainage on the environment change in permafrost regions,analyzing the long-term joint impact of multiple lakes on adjacent permafrost,simulating the near-shore talik development process and feature beneath shallow water in expanding thermokarst lakes,and continuing to do the systemic and comprehensive field measurements.