The Roman Empire fell in 476, or in 1453, depending which half you mean
Rome did not fall in one go. Its western half ended in 476 when a Germanic commander deposed a teenage emperor ironically named Romulus Augustus. The eastern half, run from Constantinople, carried on for nearly another thousand years until the city was captured in 1453.
Most of the conquering was done before there was an emperor. By 100 BC the Republic already ruled much of the Mediterranean, but civil wars tore it apart until Octavian defeated Mark Antony and Cleopatra at Actium in 31 BC and took Egypt. Four years later the Senate handed him supreme military command and the title Augustus. Provinces were split between those run by proconsuls chosen annually by lot and those owned by the emperor and governed by his legates.
Two centuries of calm followed, the Pax Romana, and the empire peaked in size under Trajan, who reigned from 98 to 117. Trouble set in under Commodus. The 3rd century brought a fifty-year crisis of civil war, plague and invasion; breakaway Gallic and Palmyrene states split off before Aurelian stitched the empire back together. Diocletian ended the civil wars and created separate courts for the Greek-speaking East and Latin West, and Constantine, the first Christian emperor, moved the capital to Byzantium in 330 and renamed it Constantinople.
In the West, migrations and invasions by Germanic peoples and the Huns wore the state down. When Ravenna fell to the Herulians and Odoacer removed Romulus Augustus, the western line of emperors stopped. The Byzantine East kept Constantinople as its only capital until 1453.
The long reach of Rome shaped language, religion, law, architecture and government across its former lands. Classical science, which also underpinned Islamic science, was rediscovered in medieval Europe and fed the Scientific Revolution, while its republican institutions inspired medieval Italian city-states, the early United States and modern republics. Even its art celebrated its self-image: a marble statue in New York's Metropolitan Museum, carved around the 1st century AD, personifies Peace.
Source: Roman Empire
