West into Europe
The known Huns moved west out of central Asia and headed eventually to Europe, adding along the way numerous tribes and ethnic groups.
The Huns clashed with the Ostrogoths in the late 4th century AD, who were then living where the Ukraine now lies. This pushed the Ostrogoths and Visigoths (who lived west of the Ostrogoths, around the Carpathians/in Transylvania) into Roman territory and is regarded as a significant step towards the so-called 'Dark Ages'. This incursion signals the beginning of what is now known as the "Migration Period" of the Germanic tribes, or the Völkerwanderung.
Their great leader Attila ruled the horde 434 AD - 453 AD, but after his death the weak political structure disintegrated, as his sons fought each other. The Huns were defeated by some sort of uprising around 455 AD and disappeared from the pages of history.
Image and reputation
The Romans considered the Huns to be the most barbaric of all barbarians, and found their appearance repulsive (this was in part Roman opinion of ‘oriental’ features, but also many Steppe nomads used to bind the heads of their children to distort the shape of the skull as they grew up, and would sometimes slash their own faces to leave deliberate scars). Even the Goths thought that the Huns were descended from ‘witches and evil spirits’ from the East.
The most notorious leader of the Huns was Attila (406-453), the "Scourge of God", who having put the Balkans (to the very walls of Constantinople), France, and northern Italy, to fire and the sword, and then extracted tribute from the Romans to not ravage them any more.
British and American propaganda in World War I often attacked the Germans as barbaric Huns, using the myth that the Huns were the ancestors of the Germans. That is not true. Furthermore, there is no connection between the Huns and the country of Hungary, despite the similarity of names. The Huns are not connected with the Mongols, another Asian group that invaded Europe centuries later.