Networks are structures consisting of nodes and arcs that connect the nodes. Networks can be used for various reasons such as finding the shortest path or the maximum flow, determining the distribution network or the network interdiction. In Network Interdiction Problems (NIPs) there are two sides called interdictor and evader who have conflicting objectives. While the evader wants to maximize the flow, or minimize the probability of being detected, the interdictor tries to do the opposite by interdicting the arcs or nodes of the same network. NIPs have been used in a wide range of areas such as transportation systems, military networks, communications networks, water systems, social networks or electric power systems. In the first section of this study, a basic mathematical model is introduced for maximizing the shortest path, and then in the latter section NIPs are examined separately according to their application areas.  Moreover, a detailed literature review has been made by classifying NIPs with respect to the situations such as stochastic, deterministic or dynamic by taking into account the environmental situations and the solution methods as well.