In Europe countries like the United Kingdom and Norway have official religions but it generally thought that most of the population has somesort of post-Christian mindset. Only Vatican City is thought of as a truly pious country that is a theocracy when it comes to governance in Europe. However, in Greece there is an autonomous state that is run by monks, has a closed border where only men can enter if they have permission, and time is based on Old Testament teachings.
The Autonomous Monastic State of the Holy Mountain, also known as Mount Athos, is under the sovereignty of Greece but has full governance over its internal affairs. Religiously, the monks on Mount Athos are spiritually under the authority of the (Eastern Orthodox) Patriarch of Constantinople.
The permanent population is composed of twenty-one religious communities of monks and their security details. Only men are allowed to live on the Mount Athos peninsula. Some feminists and members of the European Parliament have tried to force Mount Athos to accept women visitors but the monk government claims that since God gave the area to the Virgin Mary as her own garden, no other women can be allowed in.
Unlike the rest of Greece, days begin on Mount Athos at sunset. This follows with the Jewish tradition as set in the Old Testament. Mount Athos does used the Revised Julian Calender which is the normal Gregorian Calender but keeps Easter on the traditional Orthodox/Julian Calender dates.
The first monasteries were established during Roman times, probably since the 300s. Later flow of monks from the Middle East and participation in Church councils prove Mount Athos importance in the 700s. The various monasteries were funded and supported by the Roman Emperors in Constantinople (Byzantine Empire). When the Ottomans seized Constantinople, the monks pledged support to the Sultan and in return the various Sultans taxed yet supported the monasteries as well because of the sultans saw themselves as defenders of both Sunni Islam and Greek Christianity.
In 1913 the first of various international treaties gave Mount Athos to Greece while recognizing Mount Athos as self governing. Also in 1913 the last Christian War (war based primarily on a Christian religious issue and not material gain) was fought on the peninsula. Russian monks on Mount Athos embraced the heresy of imiaslavie. This heresy taught that God's name was "God" and knowing this would give people magic powers. Several Russian gunboats escorted a Russian Orthodox bishop who tried to have the monks denounce imiaslavie. The monks refused so Russian marines stormed the monastery and took several monks parishioner.
Today the various monk groups range from traditional to radical in their beliefs. Several groups have repeatedly denounced the Eastern Orthodox Patriarch in Constantinople because of improving relations between the patriarch and the Roman Catholic Church. Patriarch Bartholomew I has responded with trying to evict radical monks for their disobedience.
Mount Athos has an official website with a virtual tour of one of the monasteries. Meanwhile, Friends of Mount Athos has a website with information on how to visit the autonomous state.
If you have the time there is an informative but long documentary on Mount Athos below.