Ziggurats were built in Mesopotamia until Persian times when new types of religious buildings became popular.
Gradually the ziggurats decayed and the bricks were robbed for other buildings.
Many of the cities of southern Mesopotamia were abandoned, and it was not until many centuries later that ziggurats were investigated and their story uncovered!
The Kassite ziggurat at Dur Kurigalzu (14th century B.C.) with the lower platform restored.
You can read more about how that happened in the Time story....