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In this review, we survey the widespread use of numerical optimization or mathematical programming approaches to develop and produce petroleum fields for design and operations; lift gas and rate allocation; and reservoir development, planning, and management. Early applications adopted linear programming alongside heuristics. With continuous advancements in computing speed and algorithms, we have been able to formulate more complex and meaningful models including nonlinear programs and mixed-integer linear and nonlinear programs. Various formulations and solution strategies have been used including continuous and discrete optimization, stochastic programming to handle uncertainty, and metaheuristics such as genetic algorithms to increase solution quality while reducing computational load.