Reliability analysis plays a critical role in the design optimization, operation, and maintenance of tunnel structures. While classical mechanism models have been successfully used for tunnel structure reliability analysis, their limitations lie in their applicable conditions and complex calculations. Data-driven models have emerged as a new trend due to their efficiency and accuracy, finding extensive application throughout the entire process of tunnel structural reliability analysis. This paper elaborates a reliability analysis framework based on data-driven modeling, consisting of three steps: uncertainty analysis, failure analysis, and system analysis. The paper systematically reviews the characteristics, performance, and limitations of data-driven models in each step, with a focus on their applications. The paper also presents research challenges, including learning nonlinear features from sparse data, creating surrogate models for the structural system, and analyzing combinations of system failure modes. As potential solutions for future research, the utilization of GAN, GNN, DRL, and generative agents is recommended.