Pope IX leader of the Catholic Church and Patriarch Michael Cerularius leader of the Eastern Orthodox Church (which belonged to the Eastern Roman Empire, also known as Byzantine Empire) excommunicated each other from their respective churches, this event resulted as the formal separation of The Catholic Church and the Eastern Orthodox Church known as the East West Schism or Schism of 1054.
The main differences between The Catholic Church and The Byzantine Church were:
Theological:
The Eastern Church theology was based in the Greek philosophy, they focused on the divinity of Christ and study it in a more theoretical way although they believed on his humanity.
The Roman Catholic Church focused on the humanity of Christ, although they believed on his divinity. They were practical and based their theology on the Roman Law.
Geography:
The Eastern Roman Empire spread to Asia minor, Middle East and Northern Africa.
The Roman Catholic Church spread to Western Europe and Northern and Western areas of the Mediterranean.
Language:
The Byzantine Church spoke Greek or their local language, the Patriarch couldn't read letters written Latin.
The Roman Catholic Church spoke Latin and their Pope couldn't read letters written in Greek.
Personalities and Politics:
For the Roman Catholic Church the Pope is the supreme authority and he is infallible. The Pope has supreme power over the Roman Catholic Churches, Emperors and Kings.
The Eastern Orthodox Church highest authority is the Highest Bishop or Patriarch is considered as "first among the equals". He is not infallible and he has no supreme power. The Emperor is the supreme authority.
Marriage and Divorce:
In the Roman Catholic Church priests cannot marry, they are married to God, and divorce is not allowed.
In the Eastern Orthodox Church priests can marry, and divorce is allowed only on certain conditions.
In 1965, Pope Paul VI and Patriarch Athenagoras I of Constantinople removed the excommunications, but the separation of both churches remains until today.
