Here's all you need to know about the elusive group and its leader:
Self-exiled Islamic cleric Fethullah Gulen is the leader of the 'Gulen movement'.
Born in Erzurum, in eastern Turkey, in 1941, Gulen built up his reputation as a Sunni Muslim preacher with intense sermons.
For many years, Gulen and his movement had strong ties with President Tayyip Erdogan's centre-right Islamist-rooted AK Party.
After decades of partnership, Erdogan, an ambitious and popular leader, began to resent the scale of the Gulenists' influence. The fallout was cemented in 2013, after anti-graft police raids that touched on Erdogan's inner circle.
The Turkish president launched a series of purges against Gulen's followers in state institutions including the financial, organised crime, smuggling and anti-terrorism units of the police force. Some say this led to the attempted putsch on July 15 this year.
On July 15, a Turkish army faction backed by tanks and fighter jets staged an attempted coup against Erdogan but they failed and the strongman returned to Istanbul.
Gulen, who runs a network of charities and schools worldwide, has repeatedly denied involvement in the coup.
But Turkey designated Gulen's movement a "terror organisation". Ankara launched massive crackdown on alleged Gullen movement supporters.
Since July, more than 35,000 people have been detained for questioning while tens of thousands of others have been dismissed from government jobs -- including in judiciary, media, education, healthcare, military and local government.
Turkey wants the 75-year-old extradited from the United States to face trial. But Washington has said it would need evidence of the cleric's involvement and says the regular extradition process must be allowed to take its course.