Dogukan asks what nation (if any) can claim to be the blood descendants of Byzantium. The obvious answer would be Greece, but the modern state draws much more of its identity from Athens than Constantinople. In any case, though Greek was the language of Byzantium it wasn’t ‘Greek’ as we think of that term today. The best way I’ve heard it put is that Greece is like the elder brother of Byzantium’s offspring- the Balkan countries, Georgia, Armenia, Syria and Lebanon with their ancient Christian communities, the Copts in Egypt, etc.
Byzantium was always a polygot empire so no one modern nation can really claim to be a direct descendant although many have a piece of it. The truest scion- some would say a living remnant of the empire itself- is Mount Athos; administratively separate from modern Greece, it still keeps Byzantine time and flies the imperial flag.
In some ways it’s easier to trace individual Byzantines. I’ve met descendants of Basil I and Isaac Angelus, and the ex-King of Greece Constantine II traces his line back to Alexius I and John Tzmisces. Even Prince Philip of England has some Byzantines in the closet- he’s descended from Constantine XI through the latter’s niece Sophia. But it’s not just the high and mighty. In Greece today there are many whose names reflect their proud Byzantine origins: Xylis, Dragazis, Kedros, Lemos, Costopouloi, Dimopouloi and Stathakopouloi among many others.
I’ll end with the words of Jacques Chirac. In 2004 Turkey applied to join the EU and the objection was made that they were clearly not European in culture, tradition or religion. The former president of the French Republic defended the application with a curious argument. First he pointed out that the Ottomans had maintained Byzantine traditions, and preserved imperial chancellery habits and tax-keeping methods. Then he concluded with a verbal flourish on what it meant to be a European:
“We are all children of Byzantium.”