Because machine calculations are prone to errors that can sometimes accumulate disastrously, computer scientists use special strategies called verified computation to ensure output is reliable. Such strategies are needed for computing with probability distributions. In probabilistic calculations, analysts have routinely assumed (i) probabilities and probability distributions are precisely specified, (ii) most or all variables are independent or otherwise have well-known dependence, and (iii) model structure is known perfectly. These assumptions are usually made for mathematical convenience, rather than with empirical justification, even in sophisticated applications. Probability bounds analysis computes bounds guaranteed to enclose probabilities and probability distributions even when these assumptions are relaxed or removed. In many cases, results are best-possible bounds, i.e., tightening them requires additional empirical information. This paper presents an overview of probability bounds analysis as a computationally practical implementation of the theory of imprecise probabilities that represents verified computation of probabilities and distributions.