The Gelug or Gelug-pa (or dGe Lugs Pa, dge-lugs-pa, or Dgelugspa), also known as the Yellow Hat sect, is a school of Buddhism founded by Je Tsongkhapa (1357–1419), a philosopher and Tibetan religious leader. The first monastery he established was at Ganden, and to this day the Ganden Tripa is the nominal head of the school, though its most influential figure is the Dalai Lama. Allying themselves with the Mongols as a powerful patron, the Gelug emerged as the pre-eminent Buddhist school in Tibet since the end of the 16th century.

The Gelu-school was founded by Je Tsongkhapa (1357–1419). A great admirer of the Kadampa (Bka'-gdams-pa) teachings, Tsongkhapa was a promoter of the Kadam School's emphasis on the mahāyāna principle of universal compassion as the fundamental spiritual orientation. He combined this with a strong emphasis on the cultivation of in-depth insight into the doctrine of emptiness as propounded by the Indian Madhyamaka masters Nāgārjuna (2nd century) and Candrakīrti (7th century).

The Dalai Lama is a high lama in the Gelug or "Yellow Hat" branch of Tibetan Buddhism. The name is a combination of the Sino-Mongolian word далай (dalai) meaning "Ocean" and the Tibetan word བླ་མ་ bla-ma (with a silent "b") meaning "chief, high priest".

In religious terms, the Dalai Lama is believed by his devotees to be the rebirth of a long line of tulkus who are considered to be manifestations of the bodhisattva of compassion, Avalokiteśvara. Traditionally, the Dalai Lama is thought of as the latest reincarnation of a series of spiritual leaders who have chosen to be reborn in order to enlighten others. The Dalai Lama is often thought to be the leader of the Gelug School, but this position belongs officially to the Ganden Tripa, which is a temporary position appointed by the Dalai Lama who, in practice, exerts much influence. The line of Dalai Lamas began as a lineage of spiritual teachers; the 5th Dalai Lama assumed political authority over Tibet.

For certain periods between the 17th century and 1959, the Dalai Lamas sometimes directed the Tibetan government, which administered portions of Tibet from Lhasa. The 14th Dalai Lama remained the head of state for the Central Tibetan Administration ("Tibetan government in exile") until his retirement on March 14, 2011. He has indicated that the institution of the Dalai Lama may be abolished in the future, and also that the next Dalai Lama may be found outside Tibet and may be female. The Chinese government was very quick to reject this and claimed that only it has the authority to select the next Dalai Lama.