Greeks in the classical period and the following centuries report a Dorian invasion as having occurred, but many scholars today doubt that it happened at all; it's a hot topic of debate among scholars. Here's a post from an earlier AskHistorians thread to get you started, with sources:

https://www.reddit.com/r/AskHistorians/comments/23z8um/the_dorian_invasion_whats_the_truth_about_it/

Following the link to the earlier comment, too.

Hi, last week I wrote this about the Dorian invasion and its reception in modern scholarship in this thread.

The way Drews (1993) characterizes the historiography of the Doric invasion is that the notion is the result of 1920s German IE hunting. pp. 63-5:

Today the Dorians tend to be once again what they were before Maspero revamped them. The majority view of specialists in Greek dialectology is that Dorians were descended from North-Greek speakers, who in the Late Helladic period lived in the Pindus and other mountain ranges north and west of Boeotia.... Many of these North Greeks would then have come into the Peloponnese and Crete after the departure of South Greeks for Cyprus.... The old view - that the Dorian Invasion proceeded form the central Balkans, and that it occurred ca 1200 - is now maintained by only a few archaeologists and against increasing evidence to the contrary. In short, there may have been movement of people from the Balkans into Greece... during and shortly after the Catastrophe... but what movement there was must have been limited to individuals, families, and small groups of families. There is no evidence for a general migration.

As far as I'm aware, Drews is right that this is the accepted modern position. The only things I've seen addressing the Doric invasion have been to debunk it. But I'm a Latinist and historian. Maybe something slipped by me.