The discipline of Control Systems Engineering has become ubiquitous in most modern technological applications. Recently, given the advances in fields such as Reinforcement Learning, attention has been drawn to the need for solving control problems from highly complex systems in conditions loaded with uncertainty. Given this motivation, the field of Optimal and Robust Control presents itself as a feasible solution to these problems. These techniques accounts for the design of automatic controllers that manipulates a system in order to optimize an objective function, considering also the possibility for uncertainty in any aspect of this process. In this work, the main results in optimal control are revisited in detail, focusing in the classical Linear Quadratic (LQ) controllers which assumes a linear model of a system and a quadratic performance index to be minimized. The optimization discussed in this work is solved through a Dynamic Programming approach. In addition to this, optimal state estimators, namely Kalman Filter estimators, are formulated and integrated to the optimal controllers in order to deal with the uncertainty regarding the real state of a system. As building blocks for these concepts, the general results for dynamical systems modeling and control is also presented, although only the most important and recurrent theorems are described in detail. The controllers are evaluated in the light of a specific class of chemical processes, the continuous stirred tank reactors (CSTR). A specific model of a system within this class, which is highly nonlinear and loaded with uncertainty, is used in simulation as a benchmark to demonstrate the optimal and robust approach.