It seems as though from Antiquity up to the Early Modern Period steppe peoples would periodically invade China, Persia, India, and Europe. After the 15th century though, it seems like this came to a halt. While I was reading about this on wikipedia, it seemed like one factor might be the rise of "Gunpowder Empires" - the Ottomans, Safavids, and Mughals. Were these empires too technologically strong for future steppe people to conquer? Did their own roots in the steppe give them some advantage?
You're right that gunpowder played an important role in colonizing the steppe. Gunpowder allowed sedentary empires to field more men-at-arms because it required significantly less resources to arm and train an army equipped with gunpowder than an army of archers. Additionally, gunpowder allowed sedentary states – particularly Russia and its predecessor the Duchy of Moscow – to build nearly impregnable frontier fortifications around borders, river crossings, and other strategic areas.
The most important reason for the decline of the steppe was the development of strong and stable bureaucracies among the sedentary empires. Generally, steppe invasions occur when a) sedentary empires are divided and b) the steppe is united. It's a testament to the strength the Russian bureaucracy that the Time of Troubles was not marked by significant developments in the steppe.
Russian policy for colonizing the steppe generally worked by trapping the various tribes and nations into a cycle of dependency that continuously impoverished the nations making them even more dependent. Here's how it worked:
Encroaching Russian fortifications such as the Zasechnaya cherta gradually hemmed in steppe nations. This impoverished the nations by preventing them from trading with other sedentary empires and limiting the areas that they could graze their cattle.
Russia would support preferred steppe leaders with lavish gifts, weapons, and favorable trade agreements. Leaders, exiles and their family (often hostages) were always welcome to visit Russia where they were completely at the mercy of the Tzar. Once there, they were often never allowed to leave if Russia decided not to let them go and there was little that the Khans and Beys could do about it.
The weakened tribes that suffered from succession crises often turned to Russia to resolve their disputes. Over time, Russia asserted itself more and more to the point that succession could not occur without Russian consent.
Russia encroaches further causing greater impoverishment. Dependency of Gifts and trade missions becomes more critical for the Khans, and the cycle continues...
Source: Russia's Steppe Frontier: The Making of a Colonial Empire, 1500-1800 Michael Khodarkovsky