I like to check up on these topics in historical linguistics every few months, just to see if anything new and sexy has come in. Eurasiatic and Nostratic are linguistic macrofamilies, not accepted by most historical linguists, which purport to be ancestral to the recognised language families today, such as Uralic, Kartvelian, Altaic, and of course, because it's me, Indo-European (or I wouldn't much care). Some historical linguists believe they can detect echoes of those much earlier (15,000* - 10,000 BCE) languages in the reconstructed languages (6500 - 3500 BCE) that are more generally accepted, and that some of this is detectable even to average eyes and ears today.
I am very much rooting for this to be true, and even hold out hope that the Proto-World hypothesis that connects all languages back to a single family even earlier than that. As this is being studied at the Santa Fe Institute (founded by Los Alamos guys who wanted to go very general about studying complex systems), I keep thinking that one of these times I'm going to see that they made some intriguing breakthroughs. I'll keep trying. Nothing the last few times.
Genetic research has backed up the claims of the more adventurous theorists with surprising strength, but that may tell us something else. We may be at the limit of what we can tell from language, and all further improvements may come only from the hard sciences. Joseph Greenberg looks spot-on in describing the Amerind families and their origin (as he was with the African families, which linguists now grudgingly accept), as the DNA matches his predictions very well. But he had to stretch and make overclaims (or if you prefer, inspired guesses) to get there and there may be no more that can be wrung from languages in isolation. That may be why nothing much new is showing up. People who want to know the answers to those questions, may no longer overlap so much with people who want to work in linguistics. They may be going into other fields.
Another strong caution for me is that one of my favorite linguists, Larry Trask, did not believe in the macrofamilies, or at least, did not believe they had been strongly demonstrated. Trask is one of the linguists who stood sternly against Noam Chomsky on the matter of generative grammar for decades. I wrote about it last year - no, over two years ago. I may secretly like Trask mostly for that rather than more academic considerations. I would certainly rather not have been arguing across a table with the late professor Trask. He is pretty rough, even with nice people writing in to ask questions about linguistics. He was an American who ended up teaching in England. I don't know if that explains anything.
*If you noticed, yes, most of these macrofamilies, if one traces them back to when they supposedly began, do indeed hit the same wall, at the same time that the glaciers retreated and homo sapiens sapiens spread out across the landscape in the Northern Hemisphere. This would be both good news and bad for people like me, hoping that the relationships are true. It would mean they were exploding out at exactly the right time, suggesting that our back-tracing methods have some value. But it would also mean we are unlikely to be able to take it much farther.