In this talk, the robust control paradigm will be introduced where the need for explicitly addressing uncertainty in the control design process will be elucidated. In this paradigm two problems, the nominal performance and the robust performance problem will be presented. The related multi-objective engineering issues that these problems address and the solution methodology based on an optimization framework will be outlined. Functional analytic tools that transform the seemingly intractable problems into solvable problems will be developed. In conclusion, the present capabilities for addressing engineering problems followed by the recent research trends and directions of this research area will be indicated.