Advanced nuclear materials should be developed to support the new-type nuclear reactors with high economy and high safety. The nuclear materials refer to the nuclear fuels and nuclear structural materials, needing to have excellent thermo-mechanical performances under the extreme in-pile neutron-irradiation conditions. Their irradiation-induced thermo-mechanical properties are dynamically varying and generally related to the temperatures, the irradiation doses, the chemical components and the as-fabricated microstructures depending on the manufacture process parameters, posing significant challenges to their accurate modeling and precise prediction across all relevant length- and time-scales. It is widely acknowledged that characterizing and understanding these properties and behaviors demands abundant irradiation data; however, such experiments are very expensive and time-consuming. Consequently, multi-scale theoretical modeling and numerical simulations have been widely employed and are frequently reported in the literatures. Recent advances in machine learning (ML) now offer powerful, data-driven strategies to accelerate these efforts, enabling rapid property prediction, composition and fabrication-process optimization for advanced materials. This review begins by introducing the critical thermo-mechanical responses of nuclear fuels and structural materials under irradiation. Subsequently, current continuum-scale applications of ML in the research and development of advanced nuclear materials are investigated and discussed. Simultaneously, the prospects and limitations of ML in this field are evaluated. It is pointed out that ML should be combined with the advanced modeling and numerical simulation, and it is particularly important to enhance the understanding of the physical problems, select appropriate AI algorithms and incorporate necessary physical constraints with strong generalization capabilities.