There were several doctrinal disputes from the 4th century onwards. Some of them led to the calling of Ecumenical councils to try to resolve them. The Church in Egypt (Patriarchate of Alexandria) split into two groups folloing the Council of Chalcedon (451), owing to a dispute about the relation between the divine and human natures of Christ. Eventually this led to each group having its own Pope. Those that remained in communion with the other patriarchs were called "Melkites" (the king's men, because Constantinople was the city of the emperors), and are today known as the Greek Orthodox Patriarchate of Alexandria, led by Pope Petros VIII, while those who disagreed with the findings of the Council of Chalcedon are today known as the Coptic Orthodox Patriarchate of Alexandria, led by Pope Shenouda III. There was a similar split in Syria. Those who disagreed with the Council of Chalcedon are sometimes called "Oriental Orthodox" to distinguish them from the Eastern Orthodox, who accepted the Council of Chalcedon. The Oriental Orthodox are also sometimes referred to as "monophysites" or "non-Chalcedonians."
In the seventh century the areas covered by the churches of Alexandria, Antioch? and Jerusalem were conquered by Muslim Arabs, and the native Christians were treated as second-class citizens. Westerners tend to think of Christianity as dominant in society for a long period of history, but this has definitely not been the case for Christians in three of the five ancient churches, who have been in Muslim-dominated societies for 13 centuries. It was the Muslims who first opposed the Christian use of icons, though many Christians swiftly came to the same conclusion. The use of icons was defended and upheld at the Seventh Ecumenical Council. The end of that council is still celebrated as the "Triumph of Orthodoxy" in Orthodox churches today, and icons remain a central part of Orthodox faith and practice.
In the ninth and tenth centuries, Orthodoxy made great inroads into Eastern Europe and Russia. This work was made possible by the work of Saints Cyril and Methodius, who translated the Bible and many of the prayer books into Slavic. They found themselves competing with missionaries from the Roman diocese in places like Czechoslovakia and Bulgaria. After being driven out of Czechoslovakia, they were later welcomed in Bulgaria, in part because they prayed in the people's native language rather than in Latin, as the Roman priests did. Today the Russian Orthodox Church, in spite of 70 years of persecution under the atheistic government of the USSR, is the largest of the Orthodox Churches.
In the 11th century the Great Schism took place between Rome and Constantinople, which led to the Church of the West, the Roman Catholic Church, becoming distinct from the Churches of the East. There were doctrinal issues involved in the split, but they were exacerbated by cultural and linguistic differences. The split was between the Greek East and the Latin West.
In 1431, the Byzantine Empire finally fell. By this time Egypt was also under Muslim control, but Orthodoxy was very strong in Russia; and so Moscow became the new center of the church at that time.
In the sixteenth century, [Pope Gregory I]? called for a switch to the Gregorian Calendar. By then the Orthodox weren't listening to him, and so remained on the Julian Calendar. Today, many Orthodox have switched to a Revised Julian Calendar, which mostly matches the Gregorian Calendar, but places Easter and related feast days on the same day as does the Julian Calendar.
The Russian Orthodox Church sent missionaries to Alaska beginning in the 18th century. Their work eventually gave rise to the Orthodox Church in America. The Russian Orthodox Church was devastated by the Bolshevik Revolution and seventy years of Communism. One side effect was the flood of refugees from Russia and Eastern Europe to the United States, leading to the current jurisdictional mess.
Orthodox Christians believe that they have preserved apostolic succession from the first Apostles. While Rome traces its papacy back to the Apostle Peter, Alexandria traces its papacy back to [Mark the Evangelist]?, who founded the church in Alexandria in AD 40.
I don't know if much should be said about what a Divine Liturgy looks like, or their use of the liturgical calendar? Julian, Revised Julian and Gregorian Calendars? I'd love to include statistics on these and other pages about the current size of the various groups and recent growth rates and trends.