Uncertainty is an inherent characteristic that objectively exists throughout various stages of engineering structures, such as manufacturing and service, which significantly affects the load-bearing performance of the structures. This impact is particularly pronounced in the case of aerospace and aircraft equipment with high load-bearing demands and harsh service conditions. Therefore, it is crucial to account for the influence of multiple sources of uncertainties during the design stage to ensure structural safety. Among the numerous methods available for uncertainty analysis, inverse reliability analysis methods have shown certain advantages in terms of efficiency and robustness. Consequently, numerous domestic and foreign scholars have conducted extensive research in the field of high-confidence structural inverse reliability analysis and optimization methods, resulting in notable advancements such as adaptive iterative control algorithms, advanced reliability-based optimization strategies, and high-confidence design methods under insufficient samples. This paper provides a systematic summary of the progress made in domestic and foreign research on the inverse reliability analysis and optimization methods, with a particular focus on the development process and challenges faced by structural inverse reliability analysis methods, including strongly nonlinear performance functions, multiple design points, and low failure probability problems. Further, to address the small-sample problem that has long plagued the practical application of reliability methods, a systematic introduction is made focusing on the high-confidence structural reliability analysis and optimization theory. Therein, the chain of propagation from epistemic uncertainty induced by small samples to the confidence level of reliability is also discussed in details. Finally, by drawing upon the existing accomplishments and major national demands, this paper reflects upon and outlines the future research directions of structural reliability methods on the reusable needs of the aerospace equipment, with the expectation that relevant research outcomes will further facilitate the achievement of high reliability and ultimate lightweight design for aerospace and aircraft structures.