Borderlands: When ruins of an alien civilization are found on the distant border world of Pandora, the Atlas Corporation calls first dibs on the planet, settling and attempting to uncover its secrets. Rumors of a cache of alien technology called the Vault get out and the rival Dahl Corporation follows suit, claiming they're after the planet's minerals and setting up a mining industry with indentured convicts as most of its workforce. They secretly assign a science team, headed by Patricia Tannis, to find the Vault.
Atlas respond by deploying their private army, the Crimson Lance, to drive Dahl off. It works. Dahl leave in such a hurry they abandon much of their equipment, including a vessel called Sanctuary, and their indentured workforce.
Many of these freed convicts turn to banditry, with clans of them dividing up sections of the planet and taking over a settlement called Haven. (The dispossessed settlers then found New Haven). Patricia Tannis also remains behind, now bereft of funding and fellow researchers, but obsessed with discovering the aliens' secrets.
Word of the Vault attracts treasure seekers called Vault Hunters to Pandora, including Lilith (a superpowered mutant called a siren, only six of which ever exist at once), Mordecai (a sniper with a pet bird-monster called Bloodwing), Roland (a former Crimson Lance soldier), and Brick (a very large man). They're contacted by an enigmatic "Guardian Angel" who wants to help them find the Vault before anybody else does.
After the Vault Hunters discover the first of several fragments of the key needed to open the Vault, they're contacted by Commandant Steele of the Crimson Lance who wants the key for herself. As soon as they complete the key she steals it and opens the Vault, but finds that it isn't full of treasure. It's a prison for an alien creature called the Destroyer, which immediately kills her. The Vault Hunters manage to defeat the creature and Angel reveals this was her plan all along—she knew the Destroyer was the only thing in the Vault but believed it was too dangerous to be allowed to live, and this was the only chance to defeat it.
Borderlands: The Pre-Sequel: A programmer for the Hyperion Corporation named Jack learns there's another Vault on Pandora's moon, Elpis, this one definitely full of treasure, no for real this time. He puts together his own team of Vault Hunters including Athena (a former Crimson Lance assassin), Nisha (a bandit hunter), Wilhelm (a cyborg merc), and Claptrap (a shit robot), to find and open it. They're opposed by the Lost Legion—former Dahl soldiers who had already found the Vault, then decided it was safer left closed.
The Lost Legion take over Hyperion's space station Helios, powering up a weapon there called the Eye of Helios to use to destroy the moon and prevent the Vault being opened. On Elpis, the current crew of Vault Hunters befriend two of the previous crew, Lilith and Roland, as well as a bar-owner named Moxxi, and work together to prevent the moon from being blown up. They also track down an AI on an abandoned Dahl ship which Jack uses to create an army of robots.
After they take back the station, Lilith, Roland, and Moxxi betray Jack, knowing that the Eye of Helios is being powered by the eye of the Destroyer—the only part of the creature that survived—and is too powerful for Jack to keep. They sabotage it, and escape.
Jack and the Vault Hunters return to Elpis to open the Vault. Inside Jack finds an object carved with the Vault symbol. This gives him a vision of another Vault on Pandora containing a creature called the Warrior, which can be controlled by whoever opens the Vault and used to conquer the planet. At this point Lilith uses her siren powers to phase in and break the object, smashing it into Jack's face and scarring him permanently.
Borderlands 2: Jack, now wearing a mask and calling himself Handsome Jack, takes over Hyperion and uses his robot army to enforce order on Pandora while mining it for Eridium—a substance produced after the first Vault was opened—and trying to find the Vault of the Warrior. Roland, from the original Vault Hunter crew, heads a resistance to Jack's rule called the Crimson Raiders based out Sanctuary, a settlement built on the abandoned Atlas vessel.
News of this new Vault gets out and more Vault Hunters arrive on Pandora, including Maya (another of the six sirens), Zer0 (a mysterious assassin), Axton (an ex-Dahl sergeant), and Salvador (a man who can shoot two guns at once).
Handsome Jack attempts to have them killed, dumping them in the same icefield he abandoned Claptrap in after the events of the Pre-Sequel. The Vault Hunters join up with the Crimson Raiders in Sanctuary after being guided there by Angel. But when Angel sabotages Sanctuary's defenses the Crimson Raiders learn that she's a siren, and also Jack's daughter.
Jack's been keeping Angel imprisoned while he uses her powers to charge up a Vault key. She rebels against his control by directing the Vault Hunters to her location and begging them to kill her and free her from the contraption that's leeching her powers. Aided by Roland and Lilith, the Vault Hunters follow Angel's wishes until Handsome Jack arrives, kills Roland, and kidnaps Lilith.
When the Vault Hunters find him at the Vault of the Warrior, Handsome Jack has used Lilith's siren powers to finish charging the key and open the Vault. Working together they defeat both Jack and the Warrior, and find that there was something else in the Vault—a map, directing them to other planets that are home to Vaults.
Tales from the Borderlands: Rhys and Vaughn, two low-ranking Hyperion employees, travel to Pandora to buy a Vault key as part of a get-rich scheme. The key turns out to be a fake, and the whole grift orchestrated by two con artist sisters, Fiona and Sasha. When bandits take the money the sisters planned to con Rhys out of, the four reluctantly team up to get it back. Rhys, a cyborg, uploads a program into his brain he thinks will help find the bandits only to learn that he's just put an AI copy of Handsome Jack into his head.
The Jack AI leads them toward an even bigger score—another Vault, called the Vault of the Traveler, whose location can only be found by assembling a robot named Gortys. Rhys gets Jack out of his head by downloading him into Helios Station, then sending the station crashing into Pandora. Free from the AI, they assemble a team to open the Vault and defeat the Traveler, and finally a Vault turns out to be full of loot as promised.