Nuclear energy, with the advantages of high energy density, zero carbon emission, high sustainability and stable power supply, has received extensive attention from countries around the world. However, the key structural materials are exposed to long-term high-temperature and high neutron dose environment, which inevitably produces various types of irradiation damage defects, posing serious challenges to the mechanical properties and service life of the materials. Refractory highentropy alloys, with high melting points, good high-temperature mechanical properties and improved irradiation resistance properties, have good potential for applications in the structural materials of advanced high-temperature nuclear reactors. Due to the diversity of the refractory high-entropy alloys and the complexity of the principal elements in the alloys, the basic thermodynamic and kinetic properties of irradiation defects are the main directions of the current simulation research, which is crucial to the understanding of the irradiation damage resistance mechanisms. The main simulation research methods include atomic simulation methods such as first-principles calculations and molecular dynamics simulations. In recent years, with the deepening of the research, the study of irradiation damage evolution at higher spatial scales and longer time scales has also made progress. In this paper, we summarize the research progress on the energy properties of point defects and defect clusters, the generation and distribution of irradiation defects, and the diffusion and evolution of irradiation defects in refractory high-entropy alloys studied for nuclear applications. Based on the current research progress, we discuss future research directions for the computational simulation of irradiation damage in refractory high-entropy alloys.