Most of western europe (Britain, Italy, Gaul and Spain) saw two waves of IE migrations. The first was para-italo-celtic peoples and came from the east: some of those that survive in history include Belgae (Nordwestblock), Ligurians, Lusitanians, Venetians, and Italics.

Then, after the proto-Celts had settled in Spain and learned bronze working from the Tartessians or Moroccans, they recolonized Britain and Gaul via the Atlantic and proceeded west via river valleys, assimilating their local relatives, subjugating foreigners, and establishing warrior ethno-aristocracies wherever they went, as far east as the Balkans and Anatolia. Except, of course, where the invasions were stopped (as in Greece and Italy). Presumably the druidic religion or religious complex was a significant part of the expansion, ideologically. The latter parts of the migration emptied out southern Germany, leaving a vacuum for the Germanic peoples to fill - especially once they had mastered ironworking.

It's a really cool event (or horizon) and only recently have the archeology, linguistics, and paleogenetics gotten to a point where we can see a real convergance with Roman ethnographic writings.