A clear achievement of the Babylonians was that they were able to conquer and control a huge swath of territory. At its height in the eighteenth century BC, the Babylonian Empire stretched from the Mediterranean Sea to the Persian Gulf. It essentially dominated the entire Fertile Crescent as well as all the major trade routes of the Middle East.
The city of Babylon itself was quite the achievement. It was well organized, utilizing urban planning strategies that had streets laid out in a grid. There were early sewer systems and sanitation services. It is thought that it was the first city ever to have a population above two hundred thousand.
There were many notable cultural achievements of the Babylonians. Many sophisticated terracotta statues remain that depict various deities and show a high level of craftsmanship. They were also skilled astronomers who developed their own calendars by carefully charting the heavens. This involved a good grasp of mathematics and planning. Using their knowledge of the movement of celestial bodies, the Babylonians divided the day into the twenty-four-hour period which we still use today.
They were also writers and storytellers. The upper classes of Babylonian society were highly educated and literate. Almost every city had a library. They had texts relating to medicine, commerce, religion, and philosophy. We can also thank them for one of the earliest surviving works of fiction, The Epic of Gilgamesh.
Another achievement worth noting is the Babylonian system of laws. The earliest known codified laws are known as Hammurabi's Code. This system of laws improved upon the earlier laws of the Akkadians and Sumerians. It had a lasting impact on many of the legal systems to follow it.