Robust Optimization (RO) is a methodology that combines modeling and computational tools to handle optimization problems with uncertain data. The paper surveys the main results of RO applied to uncertain linear, conic quadratic, and semidefinite programming. For these cases, computationally tractable robust counterparts of uncertain problems are explicitly obtained or good approximations are proposed, making RO a useful tool for real-world applications. The paper discusses applications such as antenna design, truss topology design, and stability analysis/synthesis in uncertain dynamic systems. A case study of 90 LPs from the NETLIB collection reveals that the feasibility properties of real-world LP solutions can be severely affected by small perturbations in data, and RO can successfully overcome this issue. The methodology involves reformulating the uncertain problem into a robust counterpart, which is a semi-infinite optimization program. The major challenges are reformulating the robust counterpart as a tractable optimization problem and specifying reasonable uncertainty sets. The paper focuses on conic form problems and discusses interval and ellipsoidal uncertainty models. Examples from engineering, such as antenna design and truss topology design, illustrate the practical potential of RO. The paper also presents approximate robust counterparts for uncertain convex quadratic and semidefinite programming problems, showing their effectiveness in handling uncertainty.Robust Optimization (RO) is a methodology that combines modeling and computational tools to handle optimization problems with uncertain data. The paper surveys the main results of RO applied to uncertain linear, conic quadratic, and semidefinite programming. For these cases, computationally tractable robust counterparts of uncertain problems are explicitly obtained or good approximations are proposed, making RO a useful tool for real-world applications. The paper discusses applications such as antenna design, truss topology design, and stability analysis/synthesis in uncertain dynamic systems. A case study of 90 LPs from the NETLIB collection reveals that the feasibility properties of real-world LP solutions can be severely affected by small perturbations in data, and RO can successfully overcome this issue. The methodology involves reformulating the uncertain problem into a robust counterpart, which is a semi-infinite optimization program. The major challenges are reformulating the robust counterpart as a tractable optimization problem and specifying reasonable uncertainty sets. The paper focuses on conic form problems and discusses interval and ellipsoidal uncertainty models. Examples from engineering, such as antenna design and truss topology design, illustrate the practical potential of RO. The paper also presents approximate robust counterparts for uncertain convex quadratic and semidefinite programming problems, showing their effectiveness in handling uncertainty.