After the Gem War was over and Rose Quartz had won, the Gem rebellion shut down Kindergarten. However, one product of Kindergarten remained. This product was Amethyst. She befriended Rose and her two allies and friends at the time, Garnet and Pearl.
For the next 5000 years, Amethyst will stay by the side of the Crystal Gems, helping them protect the planet.
After 5000 years, Rose would meet a human called Greg Universe with whom she quickly fell in love with. She became pregnant with Steven a few years later and had to give up her physical form, as a part of her soul entered Steven. Amethyst and the other Crystal Gems raised Steven, with Amethyst playing the role as his older sister in some sense. She both looks out for him, but likes to tease him and leads him into fun, but often dangerous, events. She's also somewhat of a opposite of Pearl. Where as Pearl is paranoid about Steven and him going on dangerous tasks, and often gives anything to protect him, Amethyst encourages for Steven to join them and wants him to learn quickly. It's ultimately Garnet who decides which is better for what task.
The Homeworld Returns
After the events of Lapis Lazuli, whom managed to escape back to Homeworld, a being named Peridot started sending her machines to report on the planet and find and re-activate Kindergarten. The Crystal Gems continue to stop her on all accounts, until she heads for Earth with both Lapis and Jasper. Jasper subdued all the Crystal Gems with her electric stabilizer and they were imprisoned on the ship. Steven managed to escape and helped Ruby and Sapphire fuse back into Garnet, who then proceeded to defeat Jasper, while Amethyst held Peridot captive as Pearl managed the ship back to Earth.
The ship crashed on Earth and Jasper fused with Lapis, who proceeded to take control of their fusion and drag it down to the ocean, although Peridot escaped in a pod and is still somewhere on Earth. The Crystal Gems encountered her once more in Kindergarten, where Amethyst proclaimed a wish to hurt her and was followed by Pearl who said she'd help, though Peridot escaped them.
The Fusion arc
Upon realizing that Peridot fixed the communication hub and was trying to contact homeworld, the Gems reacted and went to destroy it once again. This time, Garnet didn't fuse with Amethyst to form Sugilite due to her unstable personality, and instead fused with Pearl. Together they formed Sardonyx, an elegant creature who destroyed the hub in seconds. However, the next few days, the hub had to be destroyed again as someone kept rebuilding it. Later, Amethyst and Steven discovered it was Pearl who fixed the hub as an excuse to fuse with Garnet. This made Garnet lose trust in Pearl, and even defuse in termoil of what she did. However, after her defusion back into Ruby and Sapphire, Steven convinced them to fuse again and they went back to trusting each other and, later, when trying to capture Peridot, they regained trust in Pearl.
Finally, after Peridot tried to kidnap Steven, the Gems managed to capture her. First Garnet poofed her and after Steven freed her from the bubble, they saw her true form without the limb enhancers. She, begrudgingly, befriended Steven and revealed the Homeworld's plans with the Cluster - an earthsized Gem ready to pop and destroy the planet. Now, they are working on ways to destroy the Cluster.
Powers and abilities
Like all gems, Amethyst can shapeshift, which she does often), can summon weapons out of their gems and can fuse with other gems. Amethyst's weapon is the whip, which she uses to lash out at her foes or to grab and throw objects with. She's also noted to fuse with Garnet and form Sugilite and fuse with Pearl and form Opal.