My research has focused on two inter-related questions. First, how do we model the impacts of terrorism and earthquake events on electric power systems? Second, how might we optimize investments in these systems when there are limited resources? For intentional attack we model the interaction between the offender and the operator of the network where both parties have limited budgets and behave in their own selfinterest. The problem was formulated as a multi-level mixed-integer programming problem and we implemented a Tabu search with an embedded greedy algorithm to find the optimum defense strategy. We model the regional earthquake hazard using a four step process that included an optimization problem to select a small collection of events from a candidate set, including a probability of occurrence for each event that matches the hazard. Since electric power systems are spatially distributed, their performance is driven by the joint distribution for damage of the components. Hence we estimated this distribution by constructing a collection of consequence scenarios for each earthquake scenario, where each consequence scenario identifies the level of damage to each component. For each consequence scenario, we used an economic dispatch model to predict the load shed and repair costs throughout the repair process. We expanded the analysis of the power network under the seismic risk by modeling the additional impact of cascading outages and the consequences on the air passenger transportation system due to the interdependency of both networks. We formulated the problem of selecting seismic mitigation strategies to increase resilience of electric power system to earthquake hazards as a two-stage stochastic program. We develop a custom solution procedure which we show to be computationally effective for extremely large problem instances.