In 872, Loire Vikings took Angers, using it as a base for further plundering. This allowed them to hit Ghent (879), Saxony (880), Charlemagne's palace at Aachen (881), Conde (882), and Amiens (883). In 885, a large Viking flotilla proceeded up the Seine, offering to spare Paris only if allowed unhindered passage. The area's duke refused, and a two-year siege commenced. The last strong Frankish king in the East, Emperor Charles the Fat, was able to push them off, offering them a ransom as well as unhampered plundering in Burgundy, his enemy at the time. Viking power began to wane, as German king Arnulf defeated them at Dyle in the Netherlands in 891. They could still dominate weaker western France into the 910s. In 911, Western Frankish king Charles the Simple granted the Viking leader Rollo lands around the mouth of the Seine, soon enlarged to include Normandy. The eventual Normans also accepted Christianity and nominal vassalage to the French King. Defending the region from other Vikings, they would rise through the century from counts to dukes, and become increasingly French. By the 930s, then, the Viking menace ebbed from Europe.
The 840s to the 920s witnessed the last wave of Barbarian influx into Western and Central Europe. Each was more destructive. When the first wave of Goth, Vandal, and Alan incursions passed though Europe's heartland and continued on, they may have destroyed the Roman state, but not necessarily its society, civilization, or culture. The shorter migrations of Franks, Alamanni, and Saxons just west of the Rhine, and then into Gaul, went much farther to wreck Roman civil and political organization, and began to cut off France from the Mediterranean coast in cultural and economic matters. The third wave, consisting of Lombards, Avars, Bulgars, and Slavs, ushered in the Dark Ages for the West and Byzantium, demolishing Antiquity's commercial, and ecological bases, plundering more thoroughly than ever before, having no interest in Roman ideas, and settling the land intensely. No longer continuing migrations, the second and third wave were plundering population transplants.
In the eighth century, Europe witnessed a new invasion in the west, that of Arab and Berber Muslims into Spain. A migration of sorts, it was less destructive. Still, carrying a developing culture and universalist religious message, the Islamic arrival markedly altered Iberia's civilization. Perhaps it was a fourth wave of migrations, but of a decidedly civilized nature. The real fourth wave of Barbarian incursions into Europe occurred with the Viking and Magyar invasions that hastened Carolingian decline. They cut short the flowering of a first medieval European civilization, and were punishing to its culture in a way unlike the previous 200 years. And though the Varangians and Normans would become a part of European society, the majority of Vikings would return to the North after their conversion to Christianity. While some have called the Vikings 'traders not raiders', this seems to exaggerate their commercial tendency directed mostly at the Black Sea and Constantinople region. More probably Vikings themselves would have put it 'mostly raid and a little trade'.
The military stresses on Europe from all sides from 830-950 caused conditions guardedly described as political anarchy. It elicited a further extension of a socio-political process in train already: feudalism. Feudalism did not reach its maturity until the thirteenth century, so only its main lines will be considered here.
In most basic terms, feudalism denotes a socio-political structure based on the granting of land by a superior political power to an inferior one in return for loyalty and services primarily of a military nature. It becomes systemic when the entirety of society is structured around variegated levels of feudal relations. There are two components. The first is a relationship of sworn loyalty to the person of the superior--in this case, the lord. The personal nature of loyalty, as opposed to attachment to an institution, is Germanic in background, quite similar to the comitatus stretching back to the third century. The second component is the tenure on land conditioned on provision of specified services. This has its precedent in late Roman land law.
Since the earliest post-Roman times, counts, generals, and kings had given out lands or revenues in return for some necessary service. Often this was based on a personal loyalty that was sundered at death. A recognizable process of evolution set in from the mid-600s. Provisionally, it consisted of four phases. As later Merovingians weakened, local notables began arrogating fiscal and political prerogatives to themselves. Integral to this process was the emergence of Mayors of the Palace based on local wealth and power. Pepin of Heristal and his descendents typify this. They grew in power in part by cultivating relationships of mutual dependence with other lesser nobility in order to undermine challengers and enfeeble kings. In the process, they alienated lands from the king, and on occasion, from the church that was not in a position to oppose them.