Quantum Theory is a very successful set of rules about calculating probabilities of measurement outcomes. But what is it really about? This naive question is still open… Probably, the most basic non-classical feature of quantum theory is contextuality: the failure of conciliating the probabilities prescribed by quantum theory with averaging over models with definite answers for any question. In this talk we must review the notion of contextuality and its exclusivity-graph approach, introduced by Cabello, Severini, and Winter. Then we will elaborate on the question: can the exclusivity principle generate the same set of correlations of quantum theory?