The Western half of the Roman Empire collapsed in the fifth century but the Eastern half continued for another thousand years until the Ottoman Empire captured Constantinople in 1453.

A sibling commentator points out that the Catholic church still uses the term “Pontifex Maximus” to refer to their pope. However, this was a title used by the dominant high priest of pre-Christian Rome and the Catholic church only started doing this after Constantine XI (last Roman emperor) died when Constantinople fell to the Turks.

The Catholic church was just one of many entities that appropriated the titles and symbols of classical Rome as a way to confer themselves with the prestige and historical legacy of the Roman Empire. For example, the words “Tsar” (Slavic), “Kaiser” (German) and “Keizer” (Dutch) are all derivations of Caesar (as a synonym for emperor). Western European rulers adopted the Roman eagle for their royal and national coat of arms; Eastern Europeans tend to prefer the double-headed variant. The most egregious example is the Holy Roman Empire which famously was neither holy nor Roman. Arguably, in its latter days, it was more a federation than an empire.

The pope does hold a title, "pontifex maximus", that is older than Christianity itself and goes back to the foundation of Rome. For a while it was unified with the emperor seat.

It fell, (quite violently, in fact) in the third century. The rest was pretense.

THE EMPIRE NEVER ENDED - PKD

Eh, it’s more like they attached themselves to the Romans for marketing purposes. Same with the Holy Roman Empire