Are Europeans mostly descended from Proto-Indo-Europeans or pre-Indo-European people?

The Proto-Indo-Europeans came from the Pontic-Caspian steppe and expanded into Europe and western Asia. Many Europeans claim to be descended from these people, but wouldn't most Europeans be descended from the people who lived in Europe prior to the Indo-European migrations? I mean, what happened to those people? Also, did the Proto-Indo-Europeans look most like Nordics or Latins or Slavs?