In 331 BC, Darius III was defeated by the forces of the Ancient Macedonian Greek ruler Alexander the Great at the Battle of Gaugamela, and in October, Babylon fell to the young conqueror. A native account of this invasion notes a ruling by Alexander not to enter the homes of its inhabitants.[20]
Under Alexander, Babylon again flourished as a centre of learning and commerce. But following Alexander's death in 323 BC in the palace of Nebuchadnezzar, his empire was divided amongst his generals, and decades of fighting soon began, with Babylon once again caught in the middle.
The constant turmoil virtually emptied the city of Babylon. A tablet dated 275 BC states that the inhabitants of Babylon were transported to Seleucia, where a palace was built, as well as a temple given the ancient name of Esagila. With this deportation, the history of Babylon comes practically to an end, though more than a century later, it was found that sacrifices were still performed in its old sanctuary.[21] By 141 BC, when the Parthian Empire took over the region, Babylon was in complete desolation and obscurity.
http://en.wikipedia.org/wiki/Babylon
Just read a teensy bit further in that link you gave re: Babylon.
You did! ;o)