Roman persecution of Christians
There is no real evidence of the Romans persecuting Christians before at least 97 CE, and only sporadic periods of persecution even after that. A Christian tradition holds that Nero persecuted the Christians living in Rome because he blamed them for the Great Fire, but historians have been unable to find any evidence of such persecution or even a reason for Nero to want to blame them unjustly. The alleged persecution of Christians following the great fire was never even mentioned by Christian commentators for the next several centuries.
Professor Keith Hopkins (A world full of gods: the Strange Triumph of Christianity) says that although in its early years Christianity was both illegal and at loggerheads with the state, it was largely ignored until the three purges of 250, 257 and 303- 311. When it occurred, persecution was usually because Christians refused to worship the gods, thereby risking divine wrath. Some Romans felt that the gods could be appeased by punishing Christians who overtly refused to worship them.
Christian persecution of pagans
Emperor Theodosius I made Christianity the official state religion of Rome in the 380s. Worship at pagan temples was outlawed in 391 and the Christian church, with state support, began to destroy, pillage and expropriate pagan temples. The Church also began a program of destroying books and all sources of knowledge and art that may destract the population from the worship of God. The great library at Alexandria, said to have contained over 700,000 scrolls, was burned down in 391 CE. The period now known as the Dark Ages would commence within the next century.