This paper presents a review and analysis of the research applying optimization to flotation design problems. Specifically, superstructures utilized, mathematical models, and optimization algorithms. The effect of epistemic and stochastic uncertainties are discussed. The new knowledge generated using this type of techniques are highlighted. As these techniques are not used in practice, the gaps for implementation are identified. The review leads to conclusions regarding the benefits of optimization based methods in practice and barriers to their use. Likely future developments are discussed.