Response surface methodology (RSM) is usually applied together with a factorial design to reduce the cost of experimentation and is especially useful when there are more potential factors than money to study a response. It was designed as a tool to have a lot of (partial) answers with as few experiments as possible; to detect factors that influence a response, and whether they interact, as well as finding an optimum treatment within a specific setup. On the other hand, the Taguchi method is a statistical method, also called robust design method, to improve the quality of manufactured goods, and more recently also applied to engineering. This paper presents an extensive literature review on the concept of the RSM and Taguchi methods in solvent extraction, engineering optimization and several machining process parameters.