Here is a CliffNotes version of the history of the split that I posted on another thread:
Great Schism - 1054
The Normans have taken over Sicily. While there, they suppress the Greek Rite Churches and tell them they must follow the Latin Rite. The Patriarch of Constantinople, Michael Cerularius, counters by suppressing all of the Latin Rite Churches within Constantinople. He writes a letter to Pope Leo III telling him what he’s done and also telling him that the Latin Rite use of unleavened bread is wrong. Leo is not a great Greek scholar so he gives the message to Cardinal Humbert for a reply. Humbert does and tells Cerularius that a patriarch does not tell the pope what to do. He gets no response to the letter, so Leo sends him to Constantinople. The patriarch and the emperor lets Humbert cool his heels for a while and don’t see him. In the meantime, Humbert is in a letter writing contest with some Greek monks about the use of the leaven versus unleavened bread. (Leo can do nothing during this period because he is tied up, literally, with the Normans, who have defeated him in battle.) Finally, his patience worn out, in July 1054, Humbert, without authority because Leo has died the previous April, places a bull of excommunication on the main altar of the Hagia Sophia. The patriarch responds with a bull excommunicating Leo, Humbert and those who had gone to Constantinople with him. This split lasts to the present day even though the excommunications were mutually lifted by Pope Paul VI and Patriarch Athenagoras in 1965.
This split is a great embarrassment on the Church and is in direct contradiction of Jesus’ prayer to His Father “to make them all one.” However, this split had a long background. Diocletian had split the Empire in two, East and West, so there was a view of “us versus them”. There were the difficulties in understanding the Greek and Latin languages that had caused problems in the past, there were haughty attitudes on both sides (including the Patriarchs of Constantinople trying to usurp the power from Rome), the adding of the “Filioque” to the Creed, the Donation of Pepin to the pope of lands that had formerly belonged to the Byzantines, and the Crowning of Charlemagne as emperor also provided tension between the two sides. Even though negotiations have occurred several times over the centuries, there is still no reconciliation.
I hope that this helps somewhat!
Blessings