This paper provides a comprehensive survey of Robust Optimization (RO), focusing on its computational attractiveness, modeling power, and broad applicability. RO is a field that addresses optimization problems under parameter uncertainty, aiming to construct solutions that are feasible for any realization of the uncertain parameters within a given set. The paper highlights the tractability of RO models, the conservativeness and probability guarantees of RO formulations, and the flexibility of the methodology in various applications. Key topics include: 1. **Tractability**: The paper discusses the conditions under which RO problems are tractable, such as when the nominal problem is well-solved and the uncertainty set is structured. 2. **Conservativeness and Probability Guarantees**: RO solutions are designed to be robust against parameter uncertainties, and the paper explores how to compute probabilistic guarantees for these solutions. 3. **Flexibility**: The paper illustrates the wide range of optimization classes and uncertainty sets that can be handled by RO, including linear, quadratic, and semidefinite optimization problems. The paper also presents a detailed example from portfolio selection to demonstrate the practical application of RO, comparing the performance of RO-based formulations with stochastic optimization methods. The results show that RO models can be solved efficiently and often outperform stochastic methods in terms of computational time and solution quality, especially under perturbations in the underlying model. Additionally, the paper discusses the structure and tractability results of RO, including the equivalence of robust linear optimization problems to second-order cone programs (SOCPs) and linear programs (LPs) under certain uncertainty sets. It also explores the connection between distributional ambiguity, risk measures, and uncertainty sets in RO, providing insights into how these concepts can guide the selection of appropriate uncertainty sets. Overall, the paper aims to outline the development and key aspects of RO, emphasizing its flexibility and structural properties, and to highlight its broad range of applications across various domains.This paper provides a comprehensive survey of Robust Optimization (RO), focusing on its computational attractiveness, modeling power, and broad applicability. RO is a field that addresses optimization problems under parameter uncertainty, aiming to construct solutions that are feasible for any realization of the uncertain parameters within a given set. The paper highlights the tractability of RO models, the conservativeness and probability guarantees of RO formulations, and the flexibility of the methodology in various applications. Key topics include: 1. **Tractability**: The paper discusses the conditions under which RO problems are tractable, such as when the nominal problem is well-solved and the uncertainty set is structured. 2. **Conservativeness and Probability Guarantees**: RO solutions are designed to be robust against parameter uncertainties, and the paper explores how to compute probabilistic guarantees for these solutions. 3. **Flexibility**: The paper illustrates the wide range of optimization classes and uncertainty sets that can be handled by RO, including linear, quadratic, and semidefinite optimization problems. The paper also presents a detailed example from portfolio selection to demonstrate the practical application of RO, comparing the performance of RO-based formulations with stochastic optimization methods. The results show that RO models can be solved efficiently and often outperform stochastic methods in terms of computational time and solution quality, especially under perturbations in the underlying model. Additionally, the paper discusses the structure and tractability results of RO, including the equivalence of robust linear optimization problems to second-order cone programs (SOCPs) and linear programs (LPs) under certain uncertainty sets. It also explores the connection between distributional ambiguity, risk measures, and uncertainty sets in RO, providing insights into how these concepts can guide the selection of appropriate uncertainty sets. Overall, the paper aims to outline the development and key aspects of RO, emphasizing its flexibility and structural properties, and to highlight its broad range of applications across various domains.