This paper discusses the development of interdiction optimization models and algorithms, with an emphasis on mathematical programming techniques and future research challenges in the field. After presenting basic interdiction concepts and notation, we recount the motivation and models behind founding research in the network interdiction field. Next, we examine some of the most common means of solving interdiction problems, focusing on dualization models and extended formulations solvable by row-generation techniques. We then examine contemporary interdiction problems involving incomplete information, information asymmetry, stochasticity, and dynamic play. We conclude by discussing several emerging applications in the field of network interdiction.