David Anthony’s The Horse, the Wheel, and Language: How Bronze-Age Riders from the Eurasian Steppes Shaped the Modern World is a bit dated, but it’s still a useful read. Papers such as Population genomics of Bronze Age Eurasia and Massive migration from the steppe was a source for Indo-European languages in Europe come out of the tradition that Anthony comes out of. Arguably these thinkers even underestimated the demographic impact of the people from the steppe.
If you are interested in this topic, I think you might find First Horse Warriors: The advent of horse riding changed the course of human history and the genetic makeup of humankind, worth a watch. I think the second half, in particular, will be interesting. Researchers whose names you see only in papers are interviewed. So if you want to put a face to the name, this is your chance.
I would say though that again watching this episode reinforces my point that visual medium is very low density in the information. They had to focus on a few major results and scaffold their visuals around that.
The main issue in the documentary is that researchers still debate the nature of the usage of the horse on the steppe. Anthony and Dorcas Brown have been arguing for an early date of widespread horse domestication, at least as early as 3500 BC. But others suggested a date closer to 2000 BC, around when the light war chariot was invented.
For Anthony’s opus has aged, I think you can say about it that it still seems to me the best accessible overview for all us laypeople about the archaeology of the steppe, Southeastern Europe and Central Asia of the Chalcolithic to Bronze Age, and what this can tell us about how those societies interact. As a model of IE spread, as an attempt to recreate IE society in a strong form, and as a model offering a specific process for that spread as it was written, it’s a bit less clear that it still stands up (even if some form of steppe hypothesis still seems likely).
The main mechanisms he talks about for spread, which are elite recruitment and stigmatization of non-IE tongues enabled by a participation of IE speaking in a particular high status ‘culture of honor/host-guest/patron-client and the horse’ (not his words), seem a bit less obviously supported post adna than he might have thought. Instead it seems more like not a lot of “elite recruitment” happened in many places.
Some other bits that don’t seem to have aged well, or stand as well to a high level of scrutiny are: When it comes to talking about the spread of Western IE as well, it seems a bit like he basically throws a description of more or less all the interactions of steppe and European farmer cultures of around 3200-2600 BCE at the wall and hopes something will stick, rather than offering much of a testable model. Another questionable aspect off the top of my head are if I recall using Rigvedic mythology as a window on the early Eastern Yamnaya (parallels on frequency of male burials in Eastern Yamnaya) to reconstruct their society. Eastern Yamnaya is also decribed as the core of Yamnaya culture. Now, it seems from adna that, even if steppe cultures ultimately->Indo-Aryan, and even if Sintashta is that steppe culture, that is an offshoot of the Corded Ware culture that postdates (and in the steppe replaces) Yamnaya and much later is actually attested. Hence a bit dubious to connect with much earlier pIE society. The normal problems with Tocharian and Anatolian being a bit vaguely explained as well (despite their centrality).