May 29, 1453. The Empire, that was mostly the one City, Constantinople, the old Greek city of Byzantium, fell to the Sultan Mehmed II, the Conqueror and, after 1425 years, 4 months and 13 days the Empire founded by Octavius finally ended with the death of the last Autokrator of the Romans, Constantine XI Palaiologos
Originally a greek colony, Βυζάντιον, Byzantium, was, according to legends, founded by Byzas from the ancient greek city of Megara in 667 BCE.
Then in the year 324, it was renamed the New Rome by Emperor Constantine I. It was consecrated as Constantinople, the City of Constantine in May 11, 330 CE. It was the wealthiest and largest city in Europe from the mid V century to the early XII.
But the City suffered a terrible blow in 1204, as the Fourth Crusade plundered and ruined it’s prosperity for centuries; while the Empire was re-established after a successful reconquest from the refugees in Nicaea, the city prosperity didn’t really return until after the Ottomans rule.
After May 29, 1453 and the Fall of Constantinople, there was other political entities that did proclaim themselves heir to the ancient Empire, starting with Constantinople conqueror, Sultan Mehmed II himself with his proclamation as Caesar. And of course, the Holy Roman Empire in Western Europe.
But while they tried to maintain a link with the ancient Empire, there was a, even if changing, political tradition that did link Octavius to Constantine IX as Autokrator as well a continuing (if evolving) legal tradition that did end with the Fall of Constantinople on this day of May 29, 1453 CE.
As a last mention, the Empire of Trebizond did survive as an independent polity, also a direct heir of the ancient Empire, until its conquest also by Mehmed II in 1461, but their rules had given up their claims to the Empire previously. And yet an offshoot of Trebizond itself, the Principality of Theodoro, survived until 1475 CE.
Today known as Istanbul, Byzantium has more than 15 million inhabitants.