There are two main schools of thought. The older school held that the languages arose on the steppes around 4000 BCE and were spread into Europe, Iran and India by waves of horse-riding nomads. The problem with this theory is that there is very little archaeological evidence for the entry of new people into either Europe or India in that time frame. The new theory, advanced in the 1980s by Colin Renfrew, is that the languages arose in Anatolia (modern Turkey) around 8000 BCE and spread with farming. This also has problems, of which the most obvious is that while there is plenty of evidence the farmers walked from Anatolia into Europe, there is none they walked out onto the steppes, tamed horses, invaded Iran, and then slowly turned back into settled farmers; that is, the model works a lot better heading west than heading east.
Now a new study has been carried out by New Zealanders Russell Gray and Quentin Atkinson that examines the spread of languages using software designed to track the origin and spread of epidemics. Their conclusion is that the languages originated in Anatolia between 9,800 and 7,800 years ago.
Predictably, nobody on the steppes origin side is convinced. The Times looked up David Anthony, one of the current leaders of the steppes origin side:
A key piece of their evidence is that proto-Indo-European had a vocabulary for chariots and wagons that included words for “wheel,” “axle,” “harness-pole” and “to go or convey in a vehicle.” These words have numerous descendants in the Indo-European daughter languages. So Indo-European itself cannot have fragmented into those daughter languages, historical linguists argue, before the invention of chariots and wagons, the earliest known examples of which date to 3500 B.C. This would rule out any connection between Indo-European and the spread of agriculture from Anatolia, which occurred much earlier. “I see the wheeled-vehicle evidence as a trump card over any evolutionary tree,” said David Anthony, an archaeologist at Hartwick College who studies Indo-European origins.I have to say that I am also unimpressed by this model. People don't spread like diseases do, leaping cultural and geographic boundaries with ease, so I would have been dubious even before I heard the result. Now that I know the result, I like it even less. I think the genetic data from Europe, which shows that modern Europeans have genes that come from somebody other than the Mesolithic inhabitants or the Neolithic farmers, is best explained by the Bronze Age entry of people from the steppes.
The argument continues.