Mongol-Tibetan relations in the 13th and 14th centuries

Doorda Darkhan's Tibetan campaign
Date 1240 Location Tibet Result Mongols withdrew. All Mongol generals were called back to Mongolia to appoint a successor to Ogedai Khan.
Belligerents
Mongol Empire	Tibet
Commanders and leaders
Doorda Darkhan	Leaders of the Rwa-sgreng monastery
Strength
30,000 soldiers	Unknown
Casualties and losses
Minimal (or no loss)	500

The Ligdan Khan and prince Choghtu's campaign
Date 1634-1637 Location Tibet Result Victory of Oirat's Khoshut Khanate increased power of Gelug-Buddhism and fall Karma Kagyu and fall of the campaign prince Choghtu force.
Belligerents
Khoshut Khanate Tibet by support Khoshut Khanate	Chahar Mongolian Khanate force Northern khalkha's Khanate force
Commanders and leaders
Güshi Khan	Ligdan Khan Prince Choghtu Prince Arslang Tayji
Strength
unknown	50 000
Casualties and losses
minimally	heavy

Mongol invasions of Tibet
Date 1688-1755 Location Tibet Result Victory of the Qing empire.
Belligerents
Dzungar Khanate Kokonur rebels	Qing empire
Commanders and leaders
Galdan Boshugtu Khan prince Tsewang Arabtan Galdan Tseren Khan Tsering Dhondup Loupsang Danzan	Kangxi Yongzheng Qianlong Lha-bzang Khan

There were several Mongol invasions of Tibet. The earliest is the alleged plot to invade Tibet by Genghis Khan in 1206, which is considered anachronistic; there is no evidence of Mongol-Tibetan encounters prior to the military campaign in 1240. The first confirmed campaign is the invasion of Tibet by the Mongol general Doorda Darkhan in 1240, a campaign of 30,000 troops that resulted in 500 casualties. The campaign was smaller than the full-scale invasions used by the Mongols against large empires. The purpose of this attack is unclear, and is still in debate among Tibetologists. Then in the late 1240s Mongolian prince Godan invited Sakya lama Sakya Pandita, who urged other leading Tibetan figures to submit to Mongol authority. This is generally considered to have marked the beginning of Mongol rule over Tibet, as well as the establishment of patron and priest relationship between Mongols and Tibetans. These relations were continued by Kublai Khan, who founded the Mongol Yuan dynasty and granted authority over whole Tibet to Drogön Chögyal Phagpa, nephew of Sakya Pandita. The Sakya-Mongol administrative system and Yuan administrative rule over the region lasted until the mid-14th century, when the Yuan dynasty began to crumble.

In the early 17th century, the Oirat Mongols again conquered the region and established the Khoshut Khanate. Since then the Mongols had intervened in Tibetan politics until the Qing conquest of Mongolia and Dzungaria.

According to one traditional Tibetan account, the Mongol emperor Genghis Khan plotted to invade Tibet in 1206, but was dissuaded when the Tibetans promised to pay tribute to the Mongols. Modern scholars consider the account to be anachronistic and factually wrong. Genghis' campaign was targeted at the Tangut kingdom of Western Xia, not Tibet, and there was certainly no tribute being paid to the Mongols prior to 1240. There are not evidences of interaction between the two nations prior to Doorda Darkhan's invasion in 1240.

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Wikipedia