Correct. It's generally known as the Great Schism
To better understand it, you have to understand how leadership sorted itself out in the early Christian Church. All of the Apostles were killed off, leaving a vacuum of power. In process of time, the general consensus was that a Pentarchy of the five most important bishops was the highest authority in the Church. These bishops were of the cities Constantinople, Antioch, Jerusalem, Alexandria and Rome. It may be of interest that all but Rome took the title "Patriarch" while Rome's bishop added "Pope" to his title. They mean (or came to mean) pretty much the same thing: "Presiding Father." The Eastern Church still sometimes refers to the Pope as "Patriarch of Rome."
For a good comparison, lets imagine a hypothetical future where the USA meets with huge disaster that erradicates the entire Federal Government and all of the State governments as well. The leaderless nation flounders for awhile. The mayors of New York, Chicago, Los Angeles, Washington DC and Philidelphia -- as leaders of the most important cities -- jump in and start leading. Bereft of any other leadership, it's only natural that Americans recovering from cateclism would be happy to follow their lead. Why would they care whether the mayors had any legitimate right to lead the nation, you follow any leader when there isn't any other leadership.
It should be noted that the Emperors of the Eastern and Western Empire were often viewed as the highest authority in Christendom. This traditional recognition of Imperial authority over the Church continued in the Byzantine Empire, where the Emperors remained powerful nearly a thousand years after emperors in Rome had ceased to exist. In many ways, the Pope filled the power vacuum left by the demise of Western emperors.
From the First Council of Nicaea till the mid 600 AD, the Emperors and this Pentarchy of the Five Patriarchs presided over the Christian Church.
Just after 600 AD, Jerusalem, Antioch and Alexandria all fell to the Persian Empire briefly, and were subsequently reconquered by the Byzantine Roman Empire. Then came the Islamic conquests of the Arabs. Antioch fell to the Arabs in 637 AD. Then Jerusalem fell to Arab Muslim conquest in 638 AD. Alexandria was conquered by the Arab Muslims in 641 AD. Some were reconquered, either by the Byzantines, or the Armenians or the Crusaders, but all such attempts to recover those cities were short lived. You can imagine the effect. Three of Christendom's great cities rapidly declined in their presumed authority.
This left just Constantinople and Rome. Both had their own delusions of supremacy over the whole Church. Rome had always been the more isolated of the 5 ruling Patriarchs. Constantinople repeatedly tried to assert dominance over the other Greek-speaking Patriachs: Antioch, Jerusalem and Alexandria. Seen as the non-Greek outsider, Rome often played mediator in the ensuing fights. This reinforced for both Constantinople and Rome the notion that they were supreme leader of Christendom.
It started to come to a head when Pope Nicholas attempted to remove Patriarch Photius and reappoint Ignatius as the Patriarch of Constantinople by his own authority and decree. This did not sit well with the Byzantine Roman Emperor, who was considered superior to both Pope and Patriarch of Constantinople by the Byzantines. The Pope was trying to undo something he had no right to meddle in, in the Emperor's view.
Three Councils were convened at Constantinople to sort the matter out, but it probably just made things worse. First they removed Photios as Patriarch and reinstated Ignatius. Then they re-removed Ignatius and reinstated Photios. Then the Council excommunicated Pope Nicholas and rejected his claims of supremacy. Then a new Emperor, Basil the Macedonian, came to power. He favored Ignatius. Photios was condemned as a heretic and Ignatius was reinstated as Patriarch of Constantinople. I suppose this left everyone claiming victory. The Pope and the Emperor both got their way.
It all finally came to a head in 1054 AD. Patriarch Michael I of Constantinople started things off by condemning the Western Church's "Judaistic" practice of using unleavened bread in communion (among other things). Pope Leo IX responded to the accusations by asserting his own supremacy as Pope, and sent and emissaries to deliver the Pope's letter responding to the accusations. Naturally, the Patriarch refused to accept the Pope's supreme authority. The emissaries then completed their second mission -- delivering a letter of excommunication from Pope Leo IX to Patriarch Michael I.
It should be noted that by the time these emissaries delived the letter excommunicating Michael I, Pope Leo IX had already died. Leo's emmissaries authority ceased with Leo's life, so the excommunication was technically invalid.
The official reason for excommunication was the deletion of the some words from the Nicene Creed-- which was a completely backwards accusation. The Church in Rome had added those words, known as "Filioque" to the Nicene Creed and the Eastern Churches had never recognized the addition.
From that day forward, the Patriachs of Alexandria, Jerusalem and Constantinople have remained separated from the Patriarch of Rome (the Pope). There have been numerous failed attempts to reunite East with West.
Oddly, the real ecclesiastical power in the Eastern Empire, the Emperor himself, was never excommunicated. Of course the Emperor ceased to be a factor in 1453 when the Ottoman Empire finally overtook Constantinople, slaughtering most of it's inhabitants and selling the remainder into slavery. There would never again be an Eastern Roman Emperor after that.
The succession of four Eastern Patriarchs within the Muslim ruled lands has continued unbroken till today, though obviously their authority is greatly diminished.
In a very real sense, you might consider the Pope a beneficiary of the demise of his fellow Patriarchs as well as the Emperors. The Pope effectively becomes the last man standing.