A theocratic Taliban patrol
Theocracy is a form of government where the rulers are religious leaders, or even claim divinity. In ancient pagan religions theocracy was difficult to distinguish from ordinary monarchy since many dynasties claimed divine descent. The canonical example is Ancient Egypt where the pharaoh was considered an incarnation of the god Horus. A similar system was in place in the Inca Empire.
The rise of Abrahamic religions led to formation of a different form of theocracy, where priests were rulers and imposed laws based on strict moralism. Such a system existed among the Twelve Tribes of Israel during the period of judges, and even later under monarchy the priests had tremendous influence on the government. In the Middle Ages and until the 19th century the Papal States were the leading Catholic theocracy. Some Catholic brotherhoods such as the Teutonic Knights or Knights of Saint John also had their own theocratic states, which did not survive the Protestant Reformation and Renaissance. Protestant theocracies were less common, with the only examples being John Calvin's state in Geneva and Puritan states in North America.
Since the birth of Islam, many Islamic realms were governed as caliphates. In the Information Age the only extant pure theocracies are unrecognized emirates formed by jihadists, among which the most important and long-lived is the Islamic Emirate of Afghanistan. Other contemporary attempts at theocracy are short-lived like the Islamic State of Iraq and the Levant or Islamic Emirate of Waziristan. More mainstream Muslim nations like Saudi Arabia and Iran still have strong theocratic traits, as sharia (Islamic religious code) is enforced as the law of the land.
Tibet under the Dalai Lamas until 1951 was the only example of a Buddhist theocracy.