Short answers, pulled from the story.
Genghis Khan unified the warring nomadic tribes of the Mongol steppe in 1206. This unification created a military machine that would soon reshape the world. Before this event, the region was a chaotic patchwork of competing groups like the Merkits, Tatars, Keraites, and Naimans.
Fifteen years of unusually wet and warm weather from 1211 to 1225 allowed for the breeding of massive numbers of horses. This climatic window provided the essential fuel for their cavalry-based expansion. Without this specific period of favorable weather, the logistical capacity to sustain such a vast army might have been impossible.
Nearly half a million people were killed by a single army during the conquest of Urgench. Each Mongol warrior in an army of perhaps two tumens, or 20,000 troops, was required to execute 24 people. This quota system resulted in the depopulation of large areas of Islamic Central Asia and northeastern Persia.
The Mongol siege of Baghdad occurred in 1258 and was led by Hulagu Khan. The campaign included the support of one thousand North Chinese engineer squads bringing advanced siege technology. This event marked a turning point in the history of the Islamic world.
The Battle of Ain Jalut in 1260 in southeastern Galilee saw the Muslim Bahri Mamluks defeat the Mongols. This battle decisively halted their advance for the first time. The Mamluk military was largely composed of Kipchaks, and the Golden Horde's supply of Kipchak fighters replenished the Mamluk armies.
The Mongol Empire developed in the course of the 13th century and reached its height from the Pacific to Central Europe. It was later known as the largest contiguous land empire of all time. Estimates suggest that between 20 and 60 million people were killed between 1206 and 1405 during the various campaigns.