The sustained escalation in aero-engine thrust-to-weight ratios and turbine inlet temperatures has established thermal barrier coatings (TBCs) as an indispensable solution for surpassing the intrinsic temperature limits of hot-section components and ensuring their long-term service reliability. Nevertheless, the service response of TBCs involves exceedingly complex thermo-mechanical-chemical (TMC) multi-field coupling and cross-scale damage evolution, which poses severe fundamental challenges to conventional single-scale experimental and analytical methodologies. This review systematically summarizes the advances in conventional and advanced modeling, simulation, and analysis techniques for TBC and further extends the discussion to the application of artificial intelligence (AI) technologies. The study aims to provide a systematic overview of analysis methods for TBC service behavior and structural optimization strategies for coatings and to promote the implementation of proactive maintenance strategies. The technical methods covered include thermal conductivity modeling, thermal stress simulation, crack propagation analysis, and mechanical behavior studies of TBC systems, which predominantly rely on diverse techniques such as multiscale modeling and finite element analysis. The paper focuses on the use of AI in TBC simulation, including data-driven modeling approaches and machine learning algorithms such as support vector machines, random forests, neural networks, and deep learning. The findings indicate that AI holds the potential to revolutionize TBC technology in multiple respects, encompassing material and structural design, performance optimization and prediction, condition monitoring, fault diagnosis and health management, and remaining useful life (RUL) prediction, while significantly improving prediction accuracy. Novel TBCs are anticipated to offer robust support for next-generation aero-engines to transcend temperature limits and achieve improved efficiency and reliability with ongoing advancements in the intelligent design of new materials.