This paper provides a detailed review of the state of the art in the field of network reliability analysis. The primary model treated is a stochastic network in which arcs fail randomly and independently with known failure probabilities. The inputs to the basic network reliability analysis problem consist of the network and a failure probability for each are in the network. The output is some measure of the reliability of the network. The reliability measures treated most extensively in this paper are: the two terminal measure, the probability that there exists a path between two specified nodes; the all-terminal measure the probability that the network is connected and the k-terminal measure, the probability that a specified node subset, K, is connected. In all cases the results concerning each problem's computational complexity, exact algorithms, analytic bounds and Monte Carlo methods are covered. The paper also treats more complex reliability measures including performability measures and stochastic shortest path, max flow and PERT problems. A discussion is provided on applications and using the techniques covered in practice.