We feel that it is useful to go back to the theoretical roots of importance sampling in order to be able to understand the source of speedup of the AIS-BN algorithm relative to the existing state of the art importance sampling algorithms for Bayesian networks. We first review the general idea of importance sampling in finite-dimensional integrals and how it can reduce the sampling variance. We then discuss the application of importance sampling to Bayesian networks. Readers interested in more details are directed to literature on Monte Carlo methods in computation of finite integrals, such as the excellent exposition by Rubinstein [1981] that we are essentially following in the first section.