Well, nothing. Slavic ethnogenesis is a real quagmire for a variety of reasons, especially in the effort to construct national identities - after all, what language do you speak in Podgorica? A common placement would be sometime in the 5th or 6th century, contemporaneous only (and generously) with the traditional 'fall' of Rome.

There are a decent number of references to putative Slavic groups in the 5th and 6th centuries, including Procopius' history of Justinian I, who does write of 'Slavic' invasions. But whether or not the Sclaveni or the Venethi are 'Slavic' is a more difficult question. The material culture (chiefly, bow fibulae sensu Werner) is similarly difficult to disentangle. The Primary Chronicle/Chronicle of Nestor begins in the 9th century, the same time that Cyril and Methodius are active.

Barford's Early Slavs is (in my understanding) a good resource, and he places the Sclavenes in the first half of the 6th century. He proposes four different categories that we can use to understand early Slavs: historical, archaeological, ethnographic, and linguistic, and explores the different implications of these placements.

Pavel Dolukhanov has a text on the same, but Barford cautions against it. At any rate, if you're thinking of something like the Battle of the Teutoburg Forest or the Gothic War, that predates the Slavic tribes; but the Byzantines and the Slavs most certainly interacted extensively.