Reliable modeling and prediction of the response of engineering systems under uncertainty are fundamental for their design, operation, and safety assessment. However, this process is challenged in real-world applications by complex system behavior, limited and noisy data, and the high dimensionality of uncertain model parameters. Addressing these challenges requires advanced methods for quantifying uncertainties and calibrating models based on observed data. This mini-symposium focuses on recent developments in Bayesian analysis and model calibration for solving inverse problems in engineering systems under uncertainty. It aims to bring together researchers working on theoretical developments and practical applications of Bayesian methods in uncertainty quantification, propagation, and decision-making. We invite contributions that explore theoretical or computational aspects, including sampling strategies and approximation techniques for solving Bayesian inverse problems, as well as their application to uncertainty quantification in physics-based and data-driven models. Applications to digital twins, system identification, and predictive modeling in structural systems are particularly encouraged.