Procopius claims that the White Huns live in a prosperous territory, and that they are the only Huns with fair complexions.
According to him, they do not live as nomads, do acknowledge a single king, observe a well-regulated constitution, and behave justly towards neighboring states.
He also describes the burial of their nobles in tumuli, accompanied by their closest associates.
This practice contrasts with evidence of cremation among the Chionites in Ammianus and with remains found by excavators of the European Huns and remains in some deposits ascribed to the Chionites in Central Asia.
Scholars believe that the Hephthalites constituted a second "Hunnish" wave who entered Bactria early in the fifth century, and who seem to have driven the Kidarites into Gandhara.
Istämi, who bears the title yabghu of the western part of the Gökturk Khaganate, collaborates with the Persian Sassanids to defeat and destroy the Hephthalites, who had been allies of the defunct Rouran Khaganate.
After a series of wars in the period 503–513, the Hephthalites are driven out of Persia and completely defeated in 557 by Khosrau I.
Their polity will hereafter come under the Göktürks and subsequent Western Turkic Khaganate.
This war tightens the grip of the Gökturks’ ruling Ashina clan on the Silk Road.