||The evaluation of probability integrals, such as first statistical moments (mean and covariance matrix) or probability of failure, can be assessed by a variety of methods. The problem of evaluating first statistical moments of multivariate probability density functions (PDFs) often arises in Bayesian updating problems, such as in structural model updating using dynamic data, while the calculation of probability of failure is needed in reliability analysis. Despite of the extensive research on this topic, severe efficiency and robustness problems still render the computation of such integrals often unreliable or unfeasible, especially as higher dimensional parameter spaces are considered. This thesis contributes on expanding the universe of applications for both Bayesian updating and reliability analysis in structural engineering to enable handling more complex and larger problems. This work more specifically suggests the use adaptive importance sampling procedures and other techniques for the evaluation of probability integrals when considering first statistical moments evaluation and reliability estimation. Applications of the proposed procedures are performed in model updating under a Bayesian framework and reliability analysis of structural systems.