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The reliability of engineering systems evolves over time and depends on random processes of loads and system properties. However, only a small portion of existing research in structural reliability analysis and rare event simulation addresses the time variant nature of reliability. This book addresses this gap with contributions from leading researchers, based on the Joint Committee on Structural Safety (JCSS) workshop on time-variant structural reliability analysis, held in December 2024 at the Technical University of Munich. The topics covered include analytical and simulation-based reliability methods, stochastic dynamics, surrogate modeling, sensitivity analysis, Bayesian updating using monitoring data, uncertainty quantification, non-stationary stochastic modeling under changing climatic conditions, and codified approaches for reliability-based design and assessment. The book not only offers a solid introduction to the fundamentals of time variant structural reliability theory but also provides a compendium of recent developments in the field. It serves both as a reference work for graduate students and as an accessible resource for researchers and practicing engineers.