Abstract: The general topic of this talk is Bayesian adaptive learning of excursion sets defined from a costly black-box model. This research field has received many attention in the last decades. During this talk, we will first review Gaussian Process Regression for feasible set estimation in the framework where the set to recover is defined from a numerical model with scalar values. We will exhibit that usual adaptive sampling criteria may lack of robustness, e.g., when the set to recover has several connex components. Then we will address more complex frameworks, such as the presence of uncertainties or the case of numerical models with vector outputs.