Nomads brought new technologies from the east that gained them a temporary advantage. Eventually, the Romans were able to adopt the technologies themselves. The Visigoths (1) introduced the shoulder harness, prior to which Romans had used a simple strap around the neck that restricted the horse's aeorta. The origin of this invention is uncertain, but the oldest attested horse harness is from about 300 B.C. in China. This new type of cavalry forced the Romans to focus away from infantry and towards heavy cavalry. Before they were able to do this, around the turn of the fifth century, the Romans suffered a number of heavy defeats by the Goths. The Romans began to incite Germanic, but also nomadic political rivalries, as well as paid tributes, which turned the tide. Nomads were also not good at sieges, as exemplified by the ineffectiveness of the Avars at the siege of Constantinople in 627.
The next major advancement in cavalry was the invention of the stirrup and hard soles. Its origin is also unclear, but it originated somewhere in the vicinity of Mongolia or China. Mongolia and China was the site of the most intense nomadic warfare because of their proximity and a lack of practical barriers. The Griffin and Tendril Culture brought stirrups to Hungary around 800 A.D. It was limited to this area until the Magyar invasions of Europe, which sprung another change in European cavalry tactics.
Nomads rarely ever invaded Europe voluntarily. Nomadic warfare on the steppe created demographic pressures that pushed desperate tribes into areas of western civilization (2). Broadly speaking, a confederation of nomads would be defeated in Mongolia and move to Northern Iran. Further pressures would put them in Ukraine, and eventually Hungary, where they invaded Europe. These forces also led to the influx of Turks into Central Asia that would become Mamluks, Qara Kanids, and Seljuks. Warfare in Mongolia peaked following the fall of the second Khaganate, until about 1200, and accelerated these forces. Once they entered into civilized regions, the complex process occured whereby they would assimilate.
Nomads were commendable for their speed, but they also used unconventional hit-and run tactics. They would travel in bands and attack sporadically, being quick to retreat when necessary. The use of the feigned retreat was an invention of nomadic warrior; by faking a retreat they would draw the opponents out of their formation. The Alans were especially adept at this, and had a reputation that almost made it pointless to fight them. These tactics, and especially the feigned retreat, are complicated because cavalry can easily become scattered and incoherent.
Another skill used by Scythians and Sarmatians was their ability to shoot backwards while retreating. This difficult maneuver is portrayed in the classic Scythian metal work of the steppe where the rider is shooting back over his shoulder. Hunnic people are an exception to this description of a highly specialized warrior; instead they relied on numbers, as well as other skilled cavalry like the Goths.
The Romans and Chinese were able to take advantage of political rivalries of barbarians and nomads. Their ability to ally with them by paying them tribute turned out to be a successful form of diplomacy. The Byzantines did this successfully until the fall of the Khazar Khaganate in 965. Don't forget that the nomads eventually prevailed against the Byzantine Empire by establishing the Ottoman Empire.
There is also a less understood phenomenon that played an important role in ancient history; the arrival of Semitic nomads or semi-nomads into the Mesopotamia via Syria. These include the Kish, Akkadians (who were Kish), Amorites, and Aramaeans. They formed the basis of Southern Mesopotamian, or "Babylonian", and Canaanite cultures for Millennia, and were last represented by the Chaldean Empire. Aramaic became the lingua Franca of the Middle East, and also formed the basis for the development of writing systems in India and Eastern Iran. The exodus of Arab nomads in 635 shouldn't be forgotten about, either. The Arabs were no exception to the tendency of nomads to continue their tribal rivalries after the conquest of a civilization; by 850 they had lost exclusive control of the Caliphate.
The invention of gunpowder was an obvious advantage over nomadic peoples. However, the age of exploration and the closing of the silk road ended a chapter in Asian history from which the nomads belonged to. The Iranian oasis cities along the silk road, which had played a formative role in the creation of the various nomadic empires (3), receded into obscurity, and the region became devoid of wealth.
1 Goths are included because they adopted the material culture of the Scythians, whom they conquered.
2 The arrival of the Alans in Sarmatia was triggered by the Xiongnu. Priscus the elder described the chain of events that led to the arrival of the huns in Europe. Later, the Avars were defeated by the Turks and arrived in Hungary. For the events from 740-1100, see The Migration of the Oghuz academia.edu
 Kasgari "a Turk without an Tat [Iranian] is like a head without a hat". This is exemplified in the Mongolian Empire by its administration by Khwarazmian bureaucrats. Turks and Iranians, a Historical Sketch