I wasn't sure where to post this, here seems suitable. Where did PIEs originate and who were they originally? Mainstream theory is the Kurgan urheimat, alternatives are Anatolian and/or Armenian hypothesis. Fringe one is Indian hypothesis.

I believe it is well established most PIE languages came from the steppes. Remaining issues are:

1) The Anatolian languages. This is the major problem with the Kurgan hypothesis. Anatolian languages are the oldest, before steppe package was even formed. They share no common words for key items with other IE languages.

2) Greek language. Undetermined where pre-Greeks came from. Archaelogy indicates Anatolia-Caucasus, Kurgan hypothesis would require steppe origins. Genetics of Mycenaeans do not exclude either scenario.

3) Armenian language. It has well-known connections with Phrygian, though under a south-of-the-steppes scenario Armenian would require no migration at all.

4) Indo-Iranian languages. The debate is infamous and connected with unlikely Indian hypothesis. Aside from that fringe scenario, in Kurgan hypothesis Indo-Iranians hailed from Andronovo hence north of the Caspian, otherwise they could have travelled south of the Caspian to their present locations.

My personal intuition favours something from south of the Caucasus. Years ago a famous genetics blogger coined a brilliant term "Womb of Nations" (Dienekes is sadly missing these days). Without much complications, I believe PIE were a part of this Womb of Nations. Anatolian languages separated and stayed south of the Caucasus while the main body moved north, influenced the inhabitants and then spread out as the famous steppe people.