In their westward movement the Hallstatt warriors overran Celtic peoples of their own kind, incidentally introducing the use of iron, one of the reasons for their own over-lordship.
However, in the 1st century BC there was Germanic migration toward the south and west at the expense of the Celtic peoples who then inhabited much of western Germany. The Celtic Helvetii, for example, once extended as far east as the Main River. They were later confined by the Germanic peoples to the area that is now Switzerland.
The Celts controlled Trans Alpine Gaul (Gallia Transalpina), which comprised the whole territory from the Rhine River and the Alps westward to the Atlantic. But eventually they were overcome by Germanic tribes pressing westward toward and across the Rhine, and by the Romans in the south, poised for further annexations to the north.
The Germanic onslaught was first felt in Bohemia, the land of the Boii, and in Noricum, a Celtic kingdom in the eastern Alps. The German assailants were known as the Cimbri, a people generally thought to have originated in Jutland (Denmark). A Roman army sent to the relief of Noricum in 113 BC was defeated, and thereafter the Cimbri, now joined by the Teutoni, ravaged widely in Trans Alpine Gaul, overcoming all Gaulish and Roman resistance.
On attempting to enter Italy, these German marauders were finally routed by Roman armies in 102 and 101 BC. There is no doubt that, during this period, many Celtic tribes, formerly living east of the Rhine, were forced to seek refuge west of the Rhine; and these migrations, as well as further German threats, gave Julius Caesar the opportunity in 58 BC to begin the campaigns that led to the Roman annexation of the whole of Gaul.
However, by the year 500 AD the entire western Roman Empire was under Germanic rule. Germanic Franks controlled the Celts in northeastern Gaul. The Germanic Burgundians were in the Rhône valley with the Germanic Visigoths as their western neighbors…until 507 when the Franks expelled the Visigoths from most of their Gallic possessions and pushed them into Spain where they lived until their extinction by the Muslims in 711.
The Germanic Ostrogoths established themselves in Rome and the rest of Italy and the Vandals moved into northern Africa.
Germanic Angles and Saxons migrated to England and by 500 AD their minority population ruled over the Celts who migrated here as early as 5000 BC.
In 568 the Germanic Lombards entered northern Italy, replaced the ruling Ostrogoths and lived there in an independent kingdom until they themselves were overthrown in 744 by their northern neighbors, the Germanic Franks. The areas of eastern Germany vacated by the Goths and others were filled up by the Slavs, who extended westward as far as Bohemia and the basin of the Elbe. But after the 8th century the Germans recovered eastern Germany, lower Austria, and much of Styria and Carinthia from the Slavs.
With all the conquering and assimilating of Celts by Germanic migrations did Celtic culture survive anywhere?…yes, it did, mainly in Ireland. The Romans never occupied Ireland, nor did the Anglo-Saxons who invaded Britain after the Romans withdrew in the 5th century, so the once dominant European Celtic culture survived more strongly in Ireland than anywhere else.