"... David hasted, and ran toward the army to meet the Philistine. And David put his hand in his bag, and took a stone, and slang it
, and smote the Philistine in his forehead, that the stone sunk into his forehead; and he fell upon his face to the earth" (KJV 1 Samuel 17:48-49).
The above quote is just one of many, many pieces of literature that point to the use of slings throughout history. Not only texts reference the use of slings, but also paintings, artifacts, and tapestries testify to the fact that slings are not a new innovation. At the time of this writing, the Muslims are having disputes with the Jews in Israel. As a result, I've seen men using slings on the front page of two newspapers in the last month. Slings are definately still being used in the modern world.
But, where do they come from? Really, no one knows exactly where they come from. They have been used in both the New and Old Worlds. I guess the logical way to look at the history of slings is to look at the history of projectile weapons. Of course, the oldest projectile weapon is the simple hand-thrown rock. After that comes a rock with a string attached-- you swing the rock by the string and throw the string along with the rock. The apparatus then evolved into the sling that we see today-- the rock is separated from the cord by use of a pouch. I imagine this evolution was gradual.