The Amorites or Martu arrived in Mesopotamia from the West. They are mentioned numerous times in the Old Testament as having Giants among them. They seemlessly merged into Sumarian society, with their own language and even rose in the societies they occupied.
The Amorites grew in power, controlling many cities in upper Mesopotamia and is believed to have started raiding the Sumerians in the South, so much so that Sulghi of Ur built a wall to keep them out. So the Amorites went around the wall and attacked. The Elamites seizing their opportunity attacked the Sumerians from the East eventually ending the Sumarian Empire.
The Amorites became rulers of Upper Mesoptamia and even expanded into Caanan and Syria. It is also believed that around this time the amorites build a Kingdom of Babylon.
MapMaster, via Wikimedia Commons
The Kassites took over Babylonia and the Amorites disappeared back into the fabric of the ruling society. Evidence remains of the Amorites societies existing for the next four hundred years in Caanan and Syria.