The Mongol Empire, founded by Genghis Khan in 1206, fragmented and declined over time. A major marker for the end of the unified Mongol Empire is when Kublai Khan convened a kurultai in 1260, marking the end of the centralized empire. More definitively, the Mongol-led Yuan dynasty in China fell in 1368 when it was overthrown by a Chinese rebel leader who founded the Ming dynasty. The last Yuan emperor fled and died in 1370. However, the Mongol lineage and remnants of their rule persisted in Mongolia under the Northern Yuan dynasty until about 1650, when Ejei Qaan surrendered to the Manchus, marking a final end to the Mongol political authority.

In summary:

• Centralized Mongol Empire effectively ended in 1260.
• Yuan dynasty (Mongol rule in China) ended in 1368.
• Northern Yuan dynasty in Mongolia ended around 1650.

This means the Mongol Empire's influence spanned from 1206 to as late as 1650 in fragmented forms.