A problem that has caught the attention of the community in the past decades is that of how to characterize, from more intuitive statements, the correlations that are observed in Nature. Moreover, the study has also extended to that of understanding the probability of obtaining certain outcomes when different (and perhaps incompatible) measurements are performed on a single system. In this talk I present a new framework to study these two problems (Nonlocality and Contextuality, respectively) in a unified manner. This approach is based on graph theory, which provides us with tools to study different sets of probabilistic models, such as the classical, quantum and no-signaling sets. I also discuss the Consistent Exclusivity and the Local Orthogonality principles, as candidates to bound the sets of quantum probabilistic models, and relate them to a hierarchy of probabilistic models which arises as semi-definite programs and converges into the quantum set.