Nonclassicality was introduced to examine if experimental observations can be explained with a classical theory. Although the formal definition of nonclassicality is known for several decades, there has been a lack of simple and complete criteria to check nonclassicality. In this work, some criteria are compared. Then, so-called nonclassicality quasiprobabilities are introduced, which allow a full examination of nonclassicality for any quantum state. Finally, some issues of the relation between nonclassicality and entanglement are discussed. All concepts are illustrated with experimental data.
