As an interesting aside, Ottoman tradition forbade shedding the blood of kin, so the usual route was strangulation of the emperor if he was a relative.
- Boiling alive in a large cauldron (as recently applied to journalists in Uzbekistan).
- Being rolled in a carpet and trampled by horses (presumably two things nomadic Mongols always have available).
- Pouring molten silver into the ears and eyes.
The Holy Roman Empire. Roma. Mussolini. And they all have one thing in common. They are not Roman.
Well, actually Mussolini might be a hard one to pin, but modern day Italians who significantly developed their culture through the Renaissance are definitely not the same as Ancient Romans.
Rome is at one point divided into two empires, West and East.
West Empire collapse, but East Empire keeps going with its capital at Constantinople. East Empire becomes the Byzantine Empire now.
East Empire actually ALMOST reunites with the West, and Justinian's top general, Belisarius, actually captures Rome in the mid 500's. He fails to hold the Italian peninsula for a variety of reasons, and Western Europe slips away.
The Turkish Empire then begins rising around the 1300's, one of many many trends driven by the Mongols and their invasions.
In the 1440s the Turkish Empire (the Ottomans basically), wipe out the kingdoms of Eastern Europe. Eastern Europe actually has a really rich history but unfortunately has had the thankless task of saving Europe over and over by being a "bullet sponge" for the powers on either side.
In 1453 the Ottomans capture Constantinople and begin their empire.
By the 1800s the empire falls into disrepair, and is now regarded as the "sick man of Europe". This is further compounded by choosing the wrong side in World War I. At the end of the war the Ottoman empire is dissolved by various treaties.
This leaves the remaining core of Turkey. Interestingly it also puts Iraq, Iran, and Palestine into the hands of the British, beginning a long road to the revolution in Iran, the various Israeli / Palestinian negotiations, and eventually, the war in Iraq.
TL;DR: Basically you can trace the fall of the Roman empire in the 500's to ISIS today somewhat simply.