After the death of Guyuk in 1248, a civil war broke out between the houses of the four sons of Genghis. Genghis had given a section of the empire to each of his sons, and gradually the civil war drove wedges between each section deeply enough that they became de facto independent nations. In the far west, the Golden Horde and its many successor continued to rule Russia up to the late 18th century. The Persian Ilkhanate rapidly disintegrated after 1335. The Chagatid Khanate of Central Asia lasted well into the 17th century. In fact IIRC the last ruler directly descended from Genghis Khan in that region only died in 1911.

Which brings us to the Yuan dynasty. The descendants of Tolui ruled China and Mongolia proper from around 1259 until 1368. In the 1320s, a native Han Chinese revolt began, and had completely evicted Mongol rulership from every region south of Beijing by the 1370s.

Descendants of Genghis Khan ruled over the steppe until the Manchu Qing dynasty gradually established suzerainty over Mongolia between 1639 and 1680. The Mongols maintained an honored position at the Manchu court, but by the late 19th century, they, as well as other ethnic groups within China, sort of abandoned ship.

Bogd Khan, a Tibetan and a Buddhist holy figure, ruled Mongolia between 1911 and 1924, but finally a Soviet supported communist government came to power after Mongolia had weakened itself fighting Chinese warlords. This government remained under Soviet control until 1991.

TL;DR The Mongol Empire disintegrated and the Mongolian state became so weak that other powers dominated it until just very recently.