Bayesian and evolutionary optimization are two fundamental approaches to the global optimization of black-box functions. This talk first consists in an introduction to Bayesian optimization, in particular the TREGO algorithm that has an additional, important, trust region mechanism. In addition, we discuss the remarkable complementarities between Bayesian and evolutionary optimization: how the problem is modeled, what evolutionary optimization can do for bayesian optimization and vice versa. We conclude with two principles for creating evolutionary variation operators from a Gaussian process: a crossover defined as a barycenter in features space and a Bayesian variation operator.