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In this dissertation, we consider operating and planning problems in integrated natural gas and electric power systems. Our work is motivated by the increasingly tighter interdependency between natural gas and power systems because of the increasing number of natural gas-fired units for electricity production. First, we develop a scheduling model under natural gas supply uncertainty. Second, we propose a nonlinear dynamic natural gas scheduling model and a electric power scheduling problem solved via decomposition. Then, we develop a coordinated expansion planning model of natural gas and power systems. Last, we develop a coordinated expansion planning model of storage facilities, and natural gas and power systems. We use the first scheduling model to analyze the effect of two types of natural gas-supply conditions, low-cost gas supply with availability issues and high-cost gas supply in a system with fast-ramping power load, on scheduling and dispatch decisions. These two cases mimic the situations in the ISO New England system and in the California ISO system, respectively. The second scheduling model is used to coordinate the operations of natural gas and power systems that accounts for the physics and engineering aspects of both systems, considering the interactions of the natural gas and power systems in gas supply and gas price of gas-fired units. The model for the coordinated expansion planning of natural gas and power systems is used to analyze the trade-off between building natural gas-related and other facilities. The model for the coordinated expansion planning of storage facilities, and natural gas and power systems allows analyzing the effect of storage facilities on mitigating gas supply shortage. Both planning models embody an appropriate balance between model accuracy and computational tractability and represent the uncertainty pertaining to natural gas and power load growth. Finally, we state the contribution of our work and the suggestions for future research.