Wheels probably started being used by copper miners in southeastern Europe, in the Carpathians, in the 4th millennium BC. The early wheels were wheelsets, with the wheel fixed solidly to an axle, and the axle rotating. For miners, any alternative to carrying loads of ore on their backs must have been welcome. Miners can smooth a path for their carts, so the problem of moving wheels on uneven terrain is reduced.
Several centuries later, somewhere between the Carpathians and the steppe country north of the Black Sea, another kind of wheel was developed, with the wheel rotating freely around a fixed axle. The new wheel was perfectly suited to a new way of life that developed on the steppes, where nomads followed herds of livestock. Horses might have been the flashiest part of the new lifestyle, but oxcarts, carrying family belongings from one grazing site to another, may have been just as important.
Judging by their reconstructed vocabulary, speakers of Proto-Indo-European – the ancestor of most of the languages of Europe and Northern India – were among those adopting the new technology.
(Actually, looking at the reconstructions, it looks like the adoption of the wheel may have come after Proto-Anatolian – ancestor to Hittite – had branched off from other Indo-European languages.)
Some cultures got into wheels more than others. Sub-Saharan African societies, even including cattle nomads, never adopted the wheel. In the Middle East, wheeled vehicles gave way pack camels sometime between Roman times and the Islamic period. As a result, Islamic states didn’t have to put as much effort into road building as earlier states, and the narrow streets of Islamic cities were made for camels, not carts, to traverse. Wheeled transportation was limited in Japan. And in the New World, wheels are known only from children’s toys.
Things were different in Europe and its cultural offshoots, where wheeled vehicles have exercised a hold on the imagination – especially the male imagination – right up to the present. This is from Richard Bulliet’s recent book, The Wheel: Inventions and Reinventions (p. 33):
Not only is the world racing fraternity composed almost entirely of men, but it has historically recruited very few drivers from East Asia, South Asia, the Middle East and Africa. …[T]he five-thousand-year history of wheels in Indo-European societies – specifically in Europe, including its former colonies, and North America – testifies to an affinity between vehicle driving and male identity in cultures that descend from the Proto-Indo-European linguistic tradition. Since the earliest days of wagon nomads and chariots, through the carriage revolution of the sixteenth century, and down to the automobile era, men brought up in European (and Euro-American) societies have repeatedly linked their manhood to their vehicles.