Some degree of replacement and acculturation, how much and when and where depend on the region, and there's still tons of question marks because this is all pre-history.

A recent paper in Nature indicates the Proto-Indo-European migration (and genetic contribution) to Western Europe is far larger than had previously been estimated, meaning more replacement rather than acculturation had gone on in those areas.

But as you can see in this chart (with Green being the theoretical Indo-European signature), some areas of Europe that now speak Indo-European languages have a relatively small Indo-European genetic contribution e.g. Sardinia, Greece, Spain and Albania. In these regions, we don't really know how the language spread. Did being surrounded by Indo-European speakers lead to adoption due to cultural pressure? Did Indo-Europeans integrate themselves as an elite, and their languages was picked up due to prestige?

What locations and/or time periods are you thinking of?