William H. McNeill in The Rise of the West talked about the "steppe gradient" whereby the steppe becomes progressively more arid and less fertile the farther East you go, creating a general pressure on all the steppe peoples to continually fight their way West in order to accommodate their growing population as well as the pressure from their neighbors to the East. Whichever group was farthest West at the time would spill out into Europe (McNeill didn't think the pressure was exclusively East-West, though, as there are obviously plenty of examples of steppe nomads riding over China and the East as well).

The reason these nomads were able to conquer Europe repeatedly was their possession of horses. On the steppe, rainfall is sparse and highly variable from year-to-year, making settled agricultural difficult if not impossible. But there's enough rain to support grasslands (that shift location from year to year) which highly mobile nomads can exploit by maintaining large herds of horses and other animals.

In Europe, however, most land suitable for raising crops to feed horses was already dedicated to growing crops for human consumption. This made horses very expensive to maintain and thus very rare. The horse-riding steppe raiders were generally able to go anywhere they liked, and as they moved faster than European communications traveled, they were not only difficult to defeat militarily but also impossible to even be aware of until they had come and gone.