Abstract: The aim of this article is to present a modern approach to the Dunford-Pettis theorem about the representation of linear, continuous operators on L1 with values in a Banach space by densities; as will be seen this result is nothing else but a Radon-Nikodým theorem. Moreover, a systematic investigation of these "representable" operators will be given, as well as some remarks about the rôle of the Radon-Nikodým property of Banach spaces in the theory of operator ideals. It is not possible to give all proofs: if not otherwise stated the reader may find the missing proofs in [6], in particular in section 3 and appendices B- D Ver menos