Many chemical plants produce a variety of hydrocarbon gases with fuel value. A fuel gas network (FGN) integrates and uses these fuel gases appropriately to make best use of them. FGNs are critical components of many chemical plants including liquefied natural gas (LNG) plants and refineries. However, a systematic approach to design and operate realistic FGNs is not currently available in the literature. We address the optimal synthesis of an FGN with many practical features such as auxiliary equipment (valves, pipelines, compressors, heaters/coolers, etc.), nonisobaric and nonisothermal operation, nonisothermal mixing, nonlinear fuel-quality specifications, fuel/utility costs, disposal and treatment costs, and emission standards. We develop a nonlinear program (NLP) based on a novel superstructure that embeds plausible alternatives for heating/cooling moving, mixing, and splitting. We successfully apply our model to three real-life case studies from the LNG and refinery industries to demonstrate that an FGN can save 40-50% of the total energy costs of a plant and reduce the fuel-from-feed or fuel-from-product consumptions by similar amounts. This work represents an important contribution toward conserving energy, preserving the environment, and improving plant economics using advanced techniques of process systems optimization.