The Gemara in Avoda Zara 2b says:
וכי מאחר דחזו לקמאי דלא מהני ולא מידי מ"ט עיילי סברי הנך אישתעבדו בהו בישראל ואנן לא שעבדנו בישראל מאי שנא הני דחשיבי ומאי שנא הני דלא חשיבי להו משום דהנך משכי במלכותייהו עד דאתי משיחא
The Gemara asks: But once the other nations see that every-thing said by the first ones, Rome and Persia, is completely ineffective, what is the reason that they come forward? The Gemara answers that they think: Those Empires subjugated the Jewish people, but we did not subjugate the Jewish people. The Gemara further asks: What is different about these, Rome and Persia, which were singled out explicitly, and what is different about those other empires that come afterward, which were not singled out and mentioned by name? It is because with regard to these, Rome and Persia, their kingship extends until the coming of the Messiah.
I suppose we could say that Persia today is basically Iran, but can we really say that Rome still exists today? Is the Gemara saying something other than that Rome will exist until the time of Moshiach?