The Iranian Revolution of 1979 was a decisive turn against Western influences, and a new, theocratic constitution that effectively made Ayatollah Ruhollah Khomeini dictator for life as part of a return to Islamic values. Among these was the banning of almost all Western culture, including most modern music. (With the exception of some music by Queen – the late great Freddie Mercury was of Persian descent, after all.)
Khomeini is gone now, but the bans remain in place.
Although the revolution against him began in January 1978, the Shah did not flee Iran until January of 1979. Ayatollah Khomeini returned from exile shortly thereafter, and while revolutionary and loyalist forces fought, the military declared itself neutral and sat out the fight.
On March 30 and 31, 1979, a referendum was held, and the Iranian people voted overwhelmingly to become a theocratic state. On April 1, it was proclaimed that the nation would henceforth be called the Islamic Republic of Iran, and Khomeini would be its president.