The ontology of quantum theory, with features such as superpositions, entanglement and quantum measurements, is fascinating and radically different to that of many established physical models. It gives rise to predictions of correlations in laboratory data that distinguish quantum theory in the broader landscape of physical models. In this thesis, I broadly investigate quantum correlations in several physical scenarios with various notions of classicality. The questions considered are of a broad scope, including purely foundational matters, tasks motivated by quantum information science as well as entirely applied considerations.