Gangkhar Puensum is the highest mountain in Bhutan and a strong candidate for the highest unclimbed mountain in the world with an elevation of 7,570 metres (24,836 ft) and a prominence of 2,995 metres (9,826 ft). It lies on the border with China (however, see below for disputes about its exact location). After Bhutan was opened for mountaineering in 1983 there were four expeditions that made failed summit attempts in 1985 and 1986. However, in 1998, a team successfully climbed a subsidiary peak of the mountain from Tibet.

The altitude of Gangkhar Puensum, alternative transliteration Gangkar Punsum or Gankar Punzum (meaning "3 mountain siblings"), was first measured in 1922 but, until recent years, maps of the region were not at all accurate and the mountain was shown in different locations and with markedly different heights. Indeed, because of inadequate mapping, the first team to attempt the summit was unable to find the mountain at all.

The book of the 1986 British expedition gives the mountain's height as 24,770 feet (7,550 m) and states that Gangkhar Puensum is completely inside Bhutan, whereas the nearby Kula Kangri is completely inside Tibet. Kula Kangri, 7,554 metres, is a separate mountain 30 km to the northeast which was first climbed in 1986. It is variously mapped and described as being in Tibet or Bhutan.

Since 1994 climbing of mountains in Bhutan higher than 6,000 metres has been prohibited out of respect for local spiritual beliefs, and since 2003 mountaineering has been forbidden completely. Gangkhar Puensum may keep its unique status for some time: any higher unclimbed peaks in the world are likely to be subsidiary tops, not separate mountains.