Mathematical research of terrorism has the potential to inform both scholars and policymakers. This thesis presents several projects in this emerging area: (1) an ordinarydifferential equations model of a terrorist organization focused on evaluating various counter-terrorism measures and predicting the evolution of terrorist conflicts; (2) a model of nuclear smuggling where the adversary is described as a Markov process on a transportation network and algorithms for positioning sensor arrays on the network; (3) a new formulation of nuclear smuggling that allows fast computation using approximation algorithms with performance guarantees; (4) a model for constructing cascade-resilient networks, with implications for analyzing the structure of terrorist networks, specifically their susceptibility to betrayal.