Everyone talks about the barbarian invasions during the Dark Ages, but barbarian is rather unfair. These "barbarians" had a well-developed culture, with their own laws and forms of art and codes of ethics and everything else you need to keep a people going. What the barbarians didn't have was written language, and this was fatal for their reputation because it meant that the only written descriptions we have come from their Roman enemies.
The following sections take these invading tribes one by one (which the Romans would have loved to do, if they'd ever had the chance).
Can we come and stay? The Visigoths
The Visigoths settled in Dacia (modern Romania) until the Huns drove them out. Then they asked the Roman Emperor Valens for permission to live in the Empire. The relationship ended in tears at the Battle of Hadrianople, where the Visigoths killed the Emperor Valens. The new emperor, Theodosius, made the Visigoths a deal. The Visigoths could stay within the Empire as long as they helped defend it against other tribes, like the Visigoths' old rivals the Ostrogoths.
This arrangement worked well until Theodosius died; then everything went pear-shaped. Theodosius's two sons, Arcadius in the East and Honorius in the West, didn't have a clue about governing, so it was open house for anyone wanting to scheme their way into power. The one man who was able to keep order was General Stilicho, but his enemies in the Senate had him murdered. The Visigoth king Alaric, who'd already started ravaging the eastern Empire, seized his chance and decided to do the same in the West. In A.D. 410, the Visigoths reached Rome and sacked it.
After sacking Rome, the Visigoths wandered around Italy for a while looking for somewhere to live until they gave up and headed for Gaul. The Romans let the Visigoths settle in the southwest, near Toulouse, but the Romans didn't trust them one bit and took care to stay on good terms with the Visigoths' old bogeymen, the Huns.
Heralding the horrible Huns
The Huns set up a base of sorts in Hungary, and in A.D. 444 or 445, a young prince named Attila (perhaps you've heard of Attila the Hun?) killed his brother Bleda and seized the throne for himself.
Attila took over a huge kingdom stretching from the Baltic to the Black Sea. He had a go at attacking Constantinople, but the walls were too strong, so he decided to chase the Visigoths out of their land in southern Gaul, instead.
An epic battle took place in A.D. 451 on the Catalaunian Plains near Troyes, southeast of Paris, in which the Roman General Aelius pulled off the seemingly impossible: he defeated Attila the Hun. Attila putzed around northern Italy for a while, married a German princess called Ildico, and headed back to Hungary where, in A.D. 453, he died.
Hungary isn't actually named after the Huns who made it their homeland; it was probably named after a later people, the Onunguns. But the Hungarians have never forgotten the Huns and won't hear a word said against them. Attila is a very popular name in modern Hungary, and the Hun art of horseback archery has been revived recently.
The Vandals go clubbing (in the Mediterranean)
The Vandals, who came from the Baltic area of northern Germany, do have a bit of an image problem because of their name. The Vandals' reputation may stem from that time in A.D. 406 when they caught the Romans on a bender at New Year, crossed the Rhine, and trashed the city of Mainz. But hey, it was the decline and fall of the Roman Empire — everyone was trashing Roman cities.
Eventually the Vandals settled in Spain, where they learned how to build ships and invaded North Africa. North Africa supplied Rome with almost all its corn, so whoever controlled it had Rome by the throat. The Vandals set up camp in the city of Carthage, and in A.D. 455, just to rub it in, they sailed over to Rome and sacked it — revenge for what the Romans had done to Carthage years before.
Not until A.D. 533, over a hundred years after the Vandals first crossed into Africa, did the Emperor Justinian finally defeat them, and he did to their kingdom what his ancestors had done to Carthage — destroyed it. Vandal prisoners were sold off as slaves throughout the Roman world, and the Vandal race was wiped out.