The territory of the Romans extended primarily through the region of the Mediterranean, encompassing parts of Africa, Europe, and Asia Minor. The Empire was governed by a Senate and, for most of its history, an Emperor who was sometimes referred to as "Caesar" after Julius Caesar or "Augustus" after Caesar Augustus.
Though the Empire brought many technological and societal advances into being on Earth it had a dark side that included brutal military campaigns and gladiatorial combat for public entertainment. Religious dissidents were also brutally persecuted. Rome had no sun worshippers. (TOS: "Bread and Circuses")
The planet 892-IV, which evolved according to Hodgkin's Law of Parallel Planetary Development, had a similar government to the Roman Empire, though that government persisted for much longer in the planet's evolution. The people had advanced to a state corresponding to the industrial revolution in Earth's history. (TOS: "Bread and Circuses")
In 2366, while Jean-Luc Picard contemplated the impending battle with the Borg, he wondered if the Emperor Flavius Honorius, while watching the Visigoths coming over the seventh hill, truly realized that the Roman Empire was about to fall. (TNG: "The Best of Both Worlds")