The introductory chapter to this study of Propertius 4 as a collection composed in the wake of Virgil’s death begins by highlighting some of the more obvious ways in which the elegist advertises his allusive engagement with the Eclogues, Georgics and, in particular, the Aeneid, and how the troping of this engagement as hospitality suggests a relationship that might be cooperative or antagonistic. From there it looks back to the only two Propertian elegies in which the name Vergilius features – 1.8 (ostensibly referring to the Pleiades constellation but, it is argued, punningly invoking the poet) and 2.34 (in a review of Virgil’s career to date), each constructing a relationship between elegiac and epic poetics that, as later chapters show, will be revisited in Book 4. After these preliminary case-studies the Introduction presents a history of approaches to poetic memory by way of a survey of the scholarly responses mobilized by Propertius 4 as a Virgilianizing collection. These approaches are then tested in the laboratory of elegy 4.9, a Virgilio-Propertian diptych on Hercules which, it is argued, is programmatic for allusion and intertextuality as enacted in this collection.