Yuan Dynasty

Genghis Khan gave the majority of the eastern portion of the Mongol empire to his third son, Ogedei Khan. In 1229, Ogedei was also elected the supreme Khan of the whole Mongol empire. In 1234, he destroyed the weakened Jin dynasty, which occupied northern China. Ogedei died in 1241. The control of the eastern portion was eventually passed to Kublai Khan. Kublai Khan continued to fight with the Song dynasty at the south. In 1271, Kublai Khan proclaimed the establishment of the Yuan dynasty. But it was not until 1279 that the Song dynasty was totally conquered. Below is a portrait of Kublai Khan:

It was during Kublai Khan's reign that the famous Venetian merchant Marco Polo visited China.  Marco Polo met Kublai Khan in Dadu (present-day Beijing) and remained in China for 17 years. After he returned to Europe, he wrote a book about his travels. This is an English translation of The Travels of Marco Polo (The Venetian)

Kublai Khan died in 1294. Before he died, he implemented a policy of sinicization, which was followed by his successors. Yuan rule in China began to collapse in 1344 CE when the Yellow River flooded and changed course, causing widespread droughts, flooding, and making impassable the Grand Canal (which connects the Yellow river in the north with the Yangtze River in the south). In 1351, the Red Turban Rebellion erupted in the Huai River valley, which saw the rise of Zhu Yuanzhang, a Han peasant, who eventually established the Ming dynasty (1368–1644). Below is a map of the Huai River valley:

The final years of the Yuan dynasty were marked by struggle, famine, and bitterness among the populace. In time, Kublai Khan's successors lost all influence on other Mongol lands across Asia because the Mongols beyond China saw them as too Chinese. Gradually, they lost influence in China as well. The reigns of the later Yuan emperors were short and marked by intrigues and rivalries. Uninterested in administration, they were separated from both the army and the populace, and China was torn by dissension and unrest. Outlaws ravaged the country without interference from the weakening Yuan armies.

In 1368, the army of Zhu Yuanzhang advanced to the Yuan capital Khanbaliq or Dadu (present-day Beijing). The Yuan dynasty collapsed and the Mongolians fled back to the Steppe. They regrouped and formed the Northern Yuan dynasty. Below is its territories: