Up until this point, all of Christendom was united as one holy Catholic and Apostolic church. They were physically still the same Church, but because of politics and geography, they were very much separated in spirit.
I take this time to reflect on people who break out of one church and start another. One kind of person will break off because he's a heretic and does not want anybody telling him he is wrong. The other kind live among heretics who used to be genuine but now support politically liberal issues and soon forget that Jesus is the head of the Church, not the popular opinion. But these latter churches break off and try to have all the parts that were right in the previous denomination but keep what they liked, and ultimately newly conservative denominations, given enough time, will expire and turn into man-centered liberal hotbeds, needing another reformation.
But first, the Western Church was mostly healthy, though it was going through renewals because so many of the religious career paths became corrupt with monks and priests having affairs, people buying their church office (simony), and people giving church offices to favorite relatives (nepotism).
"For some centuries, an account had been developing concerning the supposedly miraculous healing and conversion of Constantine by the bishop of Rome. The grateful Constantine was supposed to have made liberal grants of rights and territories to the bishop. These stories were combined in a document known as the Doctrine of Constantine and given wide circulation during the Middle Ages," (Cairns, 183). The Doctrine of Constantine justified the idea of popes owning land. Pepin donated land in 756, and others such as Isidore of Seville did the same in the 7th century.
Pope Nicholas I had a collection of various papal decrees in history. Later, they became known as False Decretals, also associated with Isidore of Seville. Some of these decrees probably were authentic from the time of Clement of Rome. Some were forgeries. Nobody really knows who wrote them all nor can they trace the sources. These included the Doctrine of Constantine. It established the authority of the pope over all church leaders and gave the right of the church to be free from secular control.
The West also sent missionaries to Scandinavia, which expanded the Western influence. The doctrine of the Mass was officially formulated about the time of Paschasius Radbertus in 831. He taught that the bread and wine really did change into Christ's blood and body and that the pope is the one who performed the miracle. I don't know if the Romans still think that the pope performs the miracle, but the priests have a lot to do with it. It's more of attributing divine powers such as miracles to people that Christ put in charge of his church that only belong to Christ. Aside note, I try to tell people that we Presbyterians do believe that the blood and body are really in the elements given during communion. Some people just nod, and others get seriously offended when I also say that the body and blood are in heaven where Christ has transported our spirits during that time to truly partake of him. To an extent, we still believe the same thing as the RCs, but details are different. Either way, the Eucharist is always a miracle and gift from Christ.
The monastery at Cluny began efforts to reform the corruption in the monasteries. They originally had its own abbot and was independent of other monasteries. The abbot of Cluny, however, influenced the appointing of new monasteries who were united to his leadership. This centralized all the orders under the pope and helped them to better condemn simony and nepotism and to promote clerical celibacy so that they could completely focus on the church.
Two popes, Nicholas I and Leo IX, asserted their influence over the Eastern patriarchs and held the leaders morally accountable. Between these two popes, however, was a series of people arguing over who should be pope and people taking the pope seat for themselves. Benedict XI, Sylvester III, and Gregory VI all claimed to be pope at the same time.
That's the West. The Eastern empire never fared as well. They were geographically separated from the West, and they spoke different languages and looked to different leaders. The Roman emperor never really had control over the Roman bishop. The pope held the West together during hard times. The East was unprotected and schizmatic. While the West focused on polity and had solid doctrine, the Greeks in the East mostly pondered theological problems and philosophies, never quite deciding on a doctrine. Eastern priests could marry and still can. Westerns cannot. Both sides argued over trivial matters such as when Easter should be celebrated and adding the filioque clause to the Nicene Creed. They also bickered over the use of icons and images in the church. Ultimately, in 1054, Michael Cerularius, patriarch of Constantinople, thought the West was wrong for using unleavened bread in the Eucharist. Pope Leo IX sent some cardinals to negotiate, but their opinions became more separated. Finally, both sides excommunicated each other. The Roman Catholics and Eastern Orthodox were two separate churches until the excommunication was removed in 1965. The original Schism paved the way for people to later question the church on substantial issues, not mere rituals.
Sometimes separation is a necessary evil in this world when we simply cannot live compatibly with each other. The Eastern Orthodox church followed more gnostic theology and mostly do not believe in the Christ that God revealed to us in history and in Scripture, or at least that you can know him. The West had the solid theology, although it began to crumble when people began to find differences in what the church taught and what the Bible said. Ultimately, Presbyterian tradition and theology comes from the Roman church, and we still have much in common, though the differences are significant enough that we cannot reunite yet.