The Maximum Flow Problem is a fundamental problem in operations research. This talk focuses on two problems involving computing a maximum flow. First, we present theoretical results on the Maximum Flow Network Interdiction Problem (MFNIP), where an interdictor seeks to remove arcs from a network so as to minimize the maximum flow in the remaining network. Second, we introduce an algorithm to rapidly solve an online sequence of similar maximum flow problems. As an application, we extend our algorithm to compute a robust minimum s-t cut, that is, a conservatively chosen minimum s-t cut in light of data uncertainty. We report the substantial reduction in running time from using our algorithm instead of repeatedly using an efficient black-box maximum flow solver.