Jeremiah 50 & 51 are prophetic of the downfall and overthrowing of Babylon. Many prophecies in Scripture have dual events of fulfillment. One might say that the first one of these is the "dress rehearsal" and the second one is the "real deal." This is one of those cases.

Ancient Babylon eventually was overthrown by the Medo-Persian Empire (see Nebuchadnezzar's statue). Babylon is in present-day Iraq, and Persia is present-day Iran. Jeremiah wrote about "an alliance of great nations from the land of the north" which would come against Babylon (Jeremiah 50:9).

We know that this ultimate battle will happen at the end of the age, for two reasons:

1) At that time, Israel no longer will be found guilty of their sins, because God will forgive the remnant that is remaining (Jeremiah 50:20).

2) After Babylon is destroyed, no man or animal will live it in it anymore, because it will be desolate forever (51:61,62).

Neither of these things has happened before. Israel cannot be completely forgiven of her sins until her Messiah comes to forgive them. Furthermore, after Jesus returns, Babylon never will be inhabited again. Many of the points in Jeremiah 50 & 51 are amazingly similar to Revelation 18, which without a doubt is the fall of Babylon that will take place at the very end of the age. More about the destruction of Babylon, and how it probably will occur, can be found at Gog vs. Antichrist.