This paper uses Bayesian updating of dynamic models of structures to perform all four levels of structural damage detection and assessment: damage indication, its location and severity, and its impact on the structural reliability. The numerical integration that is required in Bayesian updating is known to be computationally prohibitive for problems with high dimensions. The proposed approach uses Markov chain Monte Carlo simulation based on the Metropolis-Hastings algorithm to tackle this problem in conjunction with an adaptive concept to obtain information about the important regions of the updated probability distribution in an efficient manner. The Markov chain samples are then used to estimate the damage probabilities by statistical averaging for damage detection and assessment. The proposed approach is illustrated using the ASCE-IASC four-storey benchmark structure for various amounts of modal data that produce globally identifiable, locally identifiable and unidentifiable cases.