While the genetic findings point to a central role for the Yamnaya in spreading Indo-European languages, tipping the scales definitively in favor of some variant of the steppe hypothesis, those findings do not yet resolve the question of the homeland of the original Indo-European languages, the place where these languages were spoken before the Yamnaya so dramatically expanded. Anatolian languages known from four-thousand-year-old tablets recovered from the Hittite Empire and neighboring ancient cultures did not share the full wagon and wheel vocabulary present in all Indo-European languages spoken today. Ancient DNA available from this time in Anatolia shows no evidence of steppe ancestry similar to that in the Yamnaya (although the evidence here is circumstantial as no ancient DNA from the Hittites themselves has yet been published). This suggests to me that the most likely location of the population that first spoke an Indo-European language was south of the Caucasus Mountains, perhaps in present-day Iran or Armenia, because ancient DNA from people who lived there matches what we would expect for a source population both for the Yamnaya and for ancient Anatolians. If this scenario is right, the population sent one branch up into the steppe—mixing with steppe hunter-gatherers in a one-to-one ratio to become the Yamnaya as described earlier—and another to Anatolia to found the ancestors of people there who spoke languages such as Hittite.
David Reich. Who We Are and How We Got Here: Ancient DNA and the New Science of the Human Past. New York: Pantheon Books, 2018.
The insight that the Caucasus mountains served not only as a corridor for the spread of CHG/Neolithic Iranian ancestry but also for later gene-flow from the south also has a bearing on the postulated homelands of Proto-Indo-European (PIE) languages and documented gene-flows that could have carried a consecutive spread of both across West Eurasia. Perceiving the Caucasus as an occasional bridge rather than a strict border during the Eneolithic and Bronze Age opens up the possibility of a homeland of PIE south of the Caucasus, which itself provides a parsimonious explanation for an early branching off of Anatolian languages. Geographically this would also work for Armenian and Greek, for which genetic data also supports an eastern influence from Anatolia or the southern Caucasus. A potential offshoot of the Indo-Iranian branch to the east is possible, but the latest ancient DNA results from South Asia also lend weight to an LMBA spread via the steppe belt. The spread of some or all of the proto-Indo-European branches would have been possible via the North Caucasus and Pontic region and from there, along with pastoralist expansions, to the heart of Europe. This scenario finds support from the well attested and now widely documented 'steppe ancestry' in European populations, the postulate of increasingly patrilinear societies in the wake of these expansions (exemplified by R1a/R1b), as attested in the latest study on the Bell Beaker phenomenon.
Wang et al. "The genetic prehistory of the Greater Caucasus". bioRxiv, 2018.