Until 1054 AD Eastern Orthodoxy and Roman Catholicism were branches of the same body—the One, Holy, Catholic and Apostolic Church. This date marks an important moment in the history of all Christian denominations because it designates the very first major division in Christianity and the beginning of "denominations." Disagreement between these two branches of Christendom had already long existed, but the widening gap between the Roman and Eastern churches increased throughout the first millennium with a progression of worsening disputes.
On religious matters the two branches disagreed over issues pertaining to the nature of the Holy Spirit, the use of icons in worship and the correct date for celebrating Easter. Cultural differences played a major role too, with the Eastern mindset more inclined toward philosophy, mysticism, and ideology, and the Western outlook guided more by a practical and legal mentality.
This slow process of separation was encouraged in 330 AD when Emperor Constantine decided to move the capital of the Roman Empire to the city of Byzantium (Byzantine Empire, modern-day Turkey) and called it Constantinople. When he died his two sons divided their rule, one taking the Eastern portion of the empire and ruling from Constantinople and the other taking the western portion, ruling from Rome.
In 1054 AD a formal split occurred when Pope Leo IX (leader of the Roman branch) excommunicated the Patriarch of Constantinople, Michael Cerularius (leader of the Eastern branch), who in turn condemned the pope in mutual excommunication. Two primary disputes at the time were Rome's claim to a universal papal supremacy and the adding of the filioque to the Nicene Creed. This particular conflict is also known as the Filioque Controversy. The Latin word filioque means "and from the Son." It had been inserted into the Nicene Creed during the 6th century, thus changing the phrase pertaining to the origin of the Holy Spirit from "who proceeds from the Father" to "who proceeds from the Father and the Son." It had been added to emphasize Christ's divinity, but Eastern Christians not only objected to the altering of anything produced by the first ecumenical councils, they disagreed with its new meaning. Eastern Christians believe both the Spirit and the Son have their origin in the Father.
Michael Cerularius was the Patriarch of Constantinople from 1043 -1058 AD, during Eastern Orthodoxy's formal separation from the Roman Catholic Church. He played a prominent role in the circumstances surrounding the Great East-West Schism.
During the time of the Crusades (1095) Rome joined with the East to defend the Holy Land against the Turks, providing a ray of hope for potential reconciliation between the two churches. But by the end of the Fourth Crusade (1204), and the Sack of Constantinople by the Romans, all hope ended as the degree of hostility been the two churches continued to worsen. To the present date, the Eastern and Western churches remain divided and separate. However, in 1965, Pope Paul VI and Patriarch Athenagoras agreed to formally remove the mutual excommunication of 1054.
For more about Eastern Orthodox beliefs visit Eastern Orthodox Church - Beliefs and Practices.
(Sources: ReligiousTolerance.org, ReligionFacts.com, Orthodox Christian Information Center, and Way of Life.org.)