Exact inference in Bayesian Networks is known to be NP-hard. This is one of the major challenges in applying BN's to real world applications. Consequently a large amount of work in this area has been focused on the study of exact and approximate inference algorithms, both for learning the BN structure from the data and for propagating evidence through the network. In this talk I'll review inference algorithms on BN's and discuss some of the NP-hard complexity results.