Optimization methods represent a powerful instrument widely used in science, industry and economic applications, where each process is characterized by a certain potential to be optimized. This function, properly known as “objective function”, could be a measure of expended time, costs, profits, quality, but, in many cases, we may not know its structure or even it may be expensive to evaluate it: we talk about expensive black-box functions. Bayesian Optimization is the main optimization strategy used to solve this class of problems. It is based on two main components, a Gaussian Process, used as surrogate model for the objective function, and an acquisition function that guides the decision about the next to evaluate point.