Read Jeremiah 50-51 at Bible Gateway.
These prophecies against Babylon, along with similar ones elsewhere in Jeremiah and Isaiah, cause controversy among Bible scholars. The debate is: has this prophecy been fulfilled in history, or is it yet to come? Some of the prophecy seems to have been fulfilled already, such as:
Make the arrows bright!
Gather the shields!
The LORD has raised up the spirit of the kings of the Medes.
For His plan is against Babylon to destroy it,
Because it is the vengeance of the LORD,
The vengeance for His temple. Jer 51:11
It was the Medians in league with the Persians, who overthrew the Babylonian empire founded by Nebuchadnezzar’s father. The Medians, by the way, were well known as excellent archers (there are many references in these two chapters to the arrows which are arrayed against Babylon).
Another historical fulfillment might be:
The sea has come up over Babylon;
She is covered with the multitude of its waves.
Her cities are a desolation,
A dry land and a wilderness,
A land where no one dwells,
Through which no son of man passes. Jer 51:42-43
It seems to be a contradiction: Babylon is covered with a multitude of waves, and is also a dry land and a wilderness? The course of the Euphrates changed over time, and now the western half of the city that existed when Jeremiah delivered this prophecy, is completely under water. But the ruins of ancient Babylon, which are in Iraq, also exist in the middle of a desert.
But some of the prophecy seems to not have been fulfilled in history, for example:
“Therefore the wild desert beasts shall dwell there with the jackals,
And the ostriches shall dwell in it.
It shall be inhabited no more forever,
Nor shall it be dwelt in from generation to generation.
As God overthrew Sodom and Gomorrah
And their neighbors,” says the LORD, Jer 50:39-40
The prophecy is that God will overthrow Babylon as He overthrew Sodom and Gomorrah. He overthrew Sodom and Gomorrah in a single day, with fire and brimstone from heaven. That never happened in history — Babylon declined over time and became a heap of ruins over the course of centuries.
My belief is that these prophecies concerning Babylon are dual: they were fulfilled historically against the physical city of Babylon which is in Iraq, many of them, and they will be fulfilled in the future. Traditionally, those who have supported a future fulfillment say that the ancient city will be rebuilt and become the capital of the antichrist, which the LORD will destroy (see Rev 17 and 18).
However, I believe the future Babylon is the code name for the kingdoms of this world, the kingdoms of the nations who oppose the LORD and His Christ and His kingdom. The 70 nations descended from Noah were given a command by the LORD, to spread abroad in the earth and repopulate it, beginning in the fifth generation after the Flood (Gen 9:1, 10:25). The nations rebelled against the LORD’s command at Babel, which they built in order to prevent being scattered over the face of the earth (Gen 11:4). According to Josephus, this rebellion was instigated by Babel’s king, Nimrod (Gen 10:10), who introduced paganism among the nations and the rejection of the LORD has Creator and God.
Babel, the Hebrew name, is Babylon, the Greek name; and Babylon has become the code name throughout Scripture for the kingdoms of this world, the kingdoms of the nations, who reject God as God and His right to command men; as opposed to the kingdom of heaven, the kingdom of the one nation of Israel, who worship God as God and bow their knee to His commandments.
Compare these two Scriptures:
Flee from the midst of Babylon,
And every one save his life!
Do not be cut off in her iniquity,
For this is the time of the LORD’s vengeance;
He shall recompense her.
Babylon was a golden cup in the LORD’s hand,
That made all the earth drunk.
The nations drank her wine;
Therefore the nations are deranged. Jer 51:6-7
And he cried mightily with a loud voice, saying, “Babylon the great is fallen, is fallen, and has become a dwelling place of demons, a prison for every foul spirit, and a cage for every unclean and hated bird! For all the nations have drunk of the wine of the wrath of her fornication, the kings of the earth have committed fornication with her, and the merchants of the earth have become rich through the abundance of her luxury.” And I heard another voice from heaven saying, “Come out of her, my people, lest you share in her sins, and lest you receive of her plagues.” Rev 18:2-4
For further reading:
The Fall of Babylon: A Problem in Prophetic Interpretation
Coming out of Babylon