The Roman Empire was a large empire that existed in Europe for about eight centuries, starting several centuries before the birth of Jesus Christ. It was centred in the city of Rome, though it encompassed cities like Pompeii and Byzantium and had a presence as far as Cardiff, where a Roman fort was situated.
The Doctor visited southern Europe many times during the Roman period. He was alleged to have met, among other humans native to this time, Hannibal, (TV: Robot) Emperor Nero, (TV: The Romans) and Cleopatra. (TV: The Masque of Mandragora, The Girl in the Fireplace) He was also familiar with the accounts of Julius Caesar and Tacitus of the customs of the Celts and their Druid priests, noting them as among the few historically reliable ones, but with no great detail. (TV: The Stones of Blood) He also visited Judea during the reign of Augustus, and beat Mary and Joseph to the last room in a local inn. (TV: Voyage of the Damned)
In an alternate timeline where all of history occurred at the same time, parts of the Roman Empire were integrated into Earth in 2011. Winston Churchill was the Holy Roman Emperor, with the title of Caesar. A Senate existed, and Roman soldiers were seen. (TV: The Wedding of River Song)