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According to eastern homeland theory, prior to becoming known to the Roman world, Slavic-speaking tribes were part of the many multi-ethnic confederacies of Eurasia – such as the Sarmatian, Hun and Gothic empires. The Slavs emerged from obscurity when the westward movement of Germans in the 5th and 6th centuries CE (thought to be in conjunction with the movement of peoples from Siberia and Eastern Europe: Huns, and later Avars and Bulgars) started the great migration of the Slavs, who settled the lands abandoned by Germanic tribes fleeing the Huns and their allies: westward into the country between the Oder and the Elbe-Saale line; southward into Bohemia, Moravia, much of present-day Austria, the Pannonian plain and the Balkans; and northward along the upper Dnieper river. Perhaps some Slavs migrated with the movement of the Vandals to Iberia and north Africa.

What empires were part of the Roman world?
unanswerable