How did the Roman and Byzantine Churches begin?

The Roman Catholic Church began when early Christians took the teaching of Jesus to Rome from Jerusalem. St. Peter traveled to Rome after founding other churches. As the chief of the Apostles, he knew that his mission was to take the church to the center of the Roman Empire, which at that time ruled the world. St Paul also traveled to Rome. Both were martyred in Rome.

The Church stayed essentially an underground Church until Constantine became the ruler of the Roman empire and decreed that Christianity would be the official religion of the Roman Empire.

The Byzantine churches were founded by the Apostles and developed at the same time as the Roman church. The beliefs are the same and the liturgy is the same in all ways except externals. The Byzantine Church has a more Eastern Oriental flavor.

Roman Catholic Note:Please note that the Byzantine Rite Churches were split in two in the 11th century, and the half that stayed with Rome are technically Roman Byzantine Rite Churches. Mainly people use the Word "Roman" to mean the Latin Rite Church, that is incorrect, "Roman" Catholic includes all Rites of the Church including the Latin, Antiochene, Alexandrine, and Gallican, which are the four parent Rites, so it would include the Byzantine Rite Churches still in union with Rome.