We discuss different means for characterizing various quantum phenomena in a unified framework. Specifically, we focus on the interplay of different notions of quantumness, such as quantum-optical nonclassicality, entanglement, and others. Our studies include the representation of quantum effects via negative probabilities, so-called quasiprobability distributions, in theory and experiment. In addition, we elaborate on mappings of local forms of nonclassicality to quantum correlations for quantifying and converting different quantum properties. An outline to other unifying methodologies shall be given as well. Thus, different techniques with applications in experiments are presented which demonstrate that a manifold of quantum phenomena can be investigated in a universal picture.