This paper surveys the primary research in Robust Optimization (RO), focusing on its computational attractiveness, modeling power, and broad applicability. RO is a distinct field that focuses on traditional optimization-theoretic concepts, including algorithms, geometry, and tractability, as well as modeling power and structural results. Unlike Stochastic Optimization, which assumes a probabilistic description of uncertainty, RO uses a deterministic, set-based uncertainty model. The goal is to construct solutions that are feasible for any realization of the uncertainty in a given set. RO has gained significant attention due to its computational tractability and effectiveness in various application areas, including finance, statistics, learning, and engineering. RO is particularly useful when parameter uncertainty is not stochastic or when distributional information is not available. It provides solutions that are deterministically immune to realizations of uncertain parameters in certain sets. RO has been shown to be more computationally tractable than Stochastic Optimization, and it can provide probabilistic guarantees for the robust solution. The paper discusses several types of uncertainty sets, including ellipsoidal, polyhedral, and tail uncertainty sets, and how they can be used to trade off robustness and performance. The paper also discusses the tractability of RO models, the conservativeness of the RO formulation, and the flexibility of the framework to apply to different settings and applications. It presents a wide array of optimization classes and uncertainty sets, and considers the properties of the robust versions. The paper also illustrates the broad modeling power of RO by presenting a wide variety of applications, including portfolio selection, where RO is used to construct solutions that are feasible for any realization of the uncertainty in a given set. The paper concludes that RO provides a set of tools that may be useful in dealing with different types of uncertainties, both the "model error" or "noisy data" type as well as complex, stochastic descriptions of uncertainty in an explicit model. RO is also more broadly of use as a computationally viable way to handle uncertainty in models that are on their own quite difficult to solve. The paper emphasizes the importance of understanding and managing the tradeoffs between performance issues and problem complexity in RO.This paper surveys the primary research in Robust Optimization (RO), focusing on its computational attractiveness, modeling power, and broad applicability. RO is a distinct field that focuses on traditional optimization-theoretic concepts, including algorithms, geometry, and tractability, as well as modeling power and structural results. Unlike Stochastic Optimization, which assumes a probabilistic description of uncertainty, RO uses a deterministic, set-based uncertainty model. The goal is to construct solutions that are feasible for any realization of the uncertainty in a given set. RO has gained significant attention due to its computational tractability and effectiveness in various application areas, including finance, statistics, learning, and engineering. RO is particularly useful when parameter uncertainty is not stochastic or when distributional information is not available. It provides solutions that are deterministically immune to realizations of uncertain parameters in certain sets. RO has been shown to be more computationally tractable than Stochastic Optimization, and it can provide probabilistic guarantees for the robust solution. The paper discusses several types of uncertainty sets, including ellipsoidal, polyhedral, and tail uncertainty sets, and how they can be used to trade off robustness and performance. The paper also discusses the tractability of RO models, the conservativeness of the RO formulation, and the flexibility of the framework to apply to different settings and applications. It presents a wide array of optimization classes and uncertainty sets, and considers the properties of the robust versions. The paper also illustrates the broad modeling power of RO by presenting a wide variety of applications, including portfolio selection, where RO is used to construct solutions that are feasible for any realization of the uncertainty in a given set. The paper concludes that RO provides a set of tools that may be useful in dealing with different types of uncertainties, both the "model error" or "noisy data" type as well as complex, stochastic descriptions of uncertainty in an explicit model. RO is also more broadly of use as a computationally viable way to handle uncertainty in models that are on their own quite difficult to solve. The paper emphasizes the importance of understanding and managing the tradeoffs between performance issues and problem complexity in RO.