But not everywhere. Data from Scandinavia suggests that many hunter-gatherers there survived and interbred with invading farmers, contributing up to a third of the genes of late Neolithic people. Since farmers generally live at higher populations densities, this implies a fairly equal contribution to future genes and a whole lot of intermixing.
Distribution of the Bell Beaker Culture
The current consensus is that many elements of Bell Beaker culture originated in Portugal. Somehow they spread that culture to northern peoples, who took it up with great enthusiasm, and then intermarried with southern folk, at least at the elite level.
So it wasn't all conquest and replacement.