From 1d4chan
Rhodians, known for annihilating their enemies with high velocity rocks

Roughly one million years ago our pre-human ancestors figured out that throwing rocks at other beings hurts them and it allows you to stay away from their teeth, claws or tusks. It took quite a long time and some evolutionary changes to the brain to improve the concept, though.

Meet the sling - the most ancient ranged weapon known to mankind. At its most basic, it's just a rope with a cloth or leather pouch in the middle. You put a rock in that pouch, fold that rope in half and give it a good swing before releasing one of its ends, thus sending a stone flying at a speed much higher that you can by just throwing it with your hand. You might imagine throwing pebbles at, say, a deer would not be very lethal and thus not very good for hunting, but the point is, it doesn't need to be lethal - a good shot from a sling would cripple and slow it down, so you can come close and finish it with your spear or dagger or whatever you have. If you manage to score a headshot, you're looking at at least heavy concussion, at best an outright kill. And if you're hunting rabbits, it gets instantly lethal no matter where you hit. Come to think of it, a hunting bow isn't much more lethal, and that's for the better; crippling and slowing down prey is already enough, and with a bow you're likely putting a hole in the pelt.

Naturally, people quickly found out that it was good enough for killing or crippling their fellow humans. It didn't even need that much of an upgrade compared to hunting bows versus war bows - just get a bigger pouch to shoot bigger pebbles at people. Maybe make a rope longer to rain stones on the enemy formation from larger distance - it's not like you need that accuracy to hit a block of men standing shoulder-to-shoulder. Replace a pebble with a smaller lead bullet if you want it to shoot further, hit harder and potentially penetrate cloth and skin. And it worked fairly well.

From the Stone Age until early Medieval times, slings were actually dominating long-ranged combat for two simple reasons: cheapness and ease of training. A bow requires good-quality wood and strings, more so if you want it to be used to shoot humans wearing at least cloth armor and basic helmets to death, and it requires fairly expensive arrows to shoot. Sling? You can make three for cheaper than a single arrow, and stones are basically free. Even if you decide to use more expensive ceramic stones or lead bullets, they're still dirt cheap compared to arrows, and were even better compared to them in terms of range and lethality for many centuries (after which they weren't, then archery became more popular). To train a proper bowman you should start with a kid, while with a sling you can grab a bunch of peasants, drill them for a few months and voila - you have a working unit of ranged fighters. Chances are you wouldn't even need to train them, as many peasants would learn sling techniques on their own to hunt some rabbits or to protect sheep from the wolves. Of course they wouldn't be as accurate, but who cares if you can field two dozens of slingers for the cost of a single archer, and replace them in no time if they happen to die?

Considering all this and adding the ease with which a sling could be carried it wouldn't take much money and effort to arm and train your spearmen and swordsmen with slings too. Romans did it with their legionaries, and it basically allowed the unengaged maniples to drive off enemy skirmishers and keep them off the backs of their fellows going in Phalanx-style.

Naturally there's a reason why people continued to train expensive bowmen despite the awesomeness of the sling. First off, slings are probably the least accurate military-grade ranged weapon (maybe second-least if you include throwing axes). Secondly, they lack in damage department: while it's true that blunt damage gives zero shits about most types of armor, hitting anything but a head aren't likely to knock the target down, and apart from lead balls at direct-fire range (15-30m) it would not stick into their body, impeding their movements or incapacitating them via pain shock and blood loss like arrows do. Lastly, a volley of rocks or lead bullets flying at you is almost invisible, while a volley of arrows or bolts bloating the sky is terrifyingly visible and prone to cause panic or at least disruptions in formation, and these disruptions became more and more valuable then the actual damage as warfare progressed.

The former, of course, is bullshit once the Balearic Slingers enter the stage; those fuckers were described as having the damage output of catapults, were said to have more range and precision than recurve bows of the Romans (and this was stated by the same Romans who fought them). Legend and history say they were trained from childhood following a training regime quite strict (as in, if you didn't get good at shooting you'd STARVE to death). Hannibal and Caesar had made a lot of use of them, and considered them highly important assets.

One last bit about slings, is that they can throw things other than stones or bullets. Like vials of Greek Fire, or Chinese bombs, or grenades. In this last capacity they survived even past the Great War, showing up in professional hands during the Spanish Civil War and more notoriously the Winter War. During the Winter War sling fired Molotovs were the only Finnish weapon effective against Soviet tanks aside from spamming anti-tank mines. They only fell out of use with the introduction of sub-munition grenades and auxiliary grenade launchers, and even then you can find under-equipped armies without the aforementioned inventions trying it out with Molotov cocktails or even grenades.

There also exists a sling-like weapon called an atlatl that fired spears. It was favored by many early peoples and could whip spears faster and further than a human arm could alone. There is some evidence that they were even used to pierce the armoured hides of glyptodonts.

Fantasy and traditional games tend to ignore slings or pretend they don't exist. When they are included they are usually portrayed poorly and have close to unusable (or straight-up unusable) stats in the crunch. The only time you would see them used is in the hands of a DnD cleric when they were forbidden from using sharp weapons, or if some race (Haflings are the most common pick) get a sizeable bonus to damage or accuracy with it. You'd think Alchemists would use it to throw potions and bombs at things, but seems like no one among the writers and developers gave it a good thought. In Warhammer Fantasy, Skavenslaves get slings, but they're the only thing in the whole game that does. They are also completely useless.

Medieval Weaponry
Battleaxe - Dagger - Lance - Mace - Club
Pole-arm - Spear - Sword - Warhammer
Blowgun - Bows and Arrows - Cannon
Crossbow - Firearm - Rocket - Shuriken - Sling
Armor: Armor - Fantasy Armor - Helmet - Shield