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 comunion 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 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.
In the 11th century there was a split 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. Shortly before the Great Schism, the Orthodox Church had spread into the northern Balkans and Russia, to the Slavic lands, and 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.
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.