There always exists uncertainty and variability in structural integrity assessments arising from lack of knowledge, modeling approximations, or differences between as-manufactured components and as-operated components. This may ultimately impact on reactor lives. Such uncertainties and variabilities can be understood and quantified using probabilistic techniques together with reliability-based acceptance criteria, facilitating the quantification and management of risk. This review article provides a systematic appraisal of the latest worldwide literature and also unpublished reports from EDF UK nuclear plants, giving an overview of the existing knowledge of probabilistic/reliability structural integrity methodologies and tools from a multifaceted stance, including failure modes, problem types, material types, employed codes, correlations, and probability distributions. Structural reliability analysis at different levels is discussed, and pertinent issues on convergence testing, required number of trails, sensitivity analysis, verification of individual analyses, extremely small probabilities, reactor-wide failure probabilities, and digital twin structural integrity monitoring are elaborated.