Many years ago, the Kryptonian military leader Admiral Zod commanded a fleet of warships made of the Sunstone mineral. The fleet invaded numerous worlds in the surrounding Rao system and their modular ships proved to be completely indefatigable. 
At some indeterminate point in time, Zod's ship broke away from the fleet and made its way to the Sol system. In 1938, the ship landed in West Texas and burrowed its way deep into the Earth's core where it remained inert for several decades (whether Zod was piloting the vessel at this time remains unknown).
In recent years, criminal mastermind Lex Luthor came into possession of a small Sunstone crystal shard and managed to decipher the Kryptonian writing etched upon its side. From it, he learned about the classified UFO crash site and knew that the vessel buried deep in the Earth was of Kryptonian origin. Luthor embarked upon an ambitious plan to take control of the vessel and use it to destroy the very city he helped to build – Metropolis.
With the aid of the Toyman, Metallo and the new Kryptonite Man, Luthor was able to remotely awaken Zod's ship and take command of it. Tapping into the Sunstone's programming, he caused the mineral deposits to replicate into dozens of towering spires and modular siege weapons, which ravaged the Metropolis island of New Troy.
Unfortunately for Luthor, his arch-nemesis Superman (having only recently regained his lost super-powers), returned to active status and sought to prevent Luthor's attack on Metropolis. He smashed through the hull of Zod's ship, grabbing Luthor and wresting control of the Sunstone from him.
After sending Luthor to Stryker's Island Penitentiary, Superman disposed of all remaining traces of Sunstone, keeping the original crystal shard for himself. He flew to the Northern reaches of the Arctic and hurled the crystal across the frozen tundra. True to it's programming, the crystal took root in the ice and grew into a large trapezoidal super-structure. The structure now serves as Superman's new Fortress of Solitude. Superman has since used this crystal shard to activate a special communication console within the Fortress. Drawing upon its knowledge of all things Kryptonian, the shard has simulated a likeness of Superman's late father, Jor-El.  Whenever Superman needed guidance, he activated the shard and spoke directly to Jor-El's simalucrum, as if he were actually speaking to the real Jor-El.
Superman's cousin, Supergirl, has demonstrated the ability to generate material from her body with properties similar to that of Sunstone. Due to interaction with a crystal during infancy, Supergirl unconsciously produces Sunstone from her body whenever she experiences grave injury. Her first experience with this ability took place during a battle with the League of Assassins leader, Batgirl. 
Superman has used Sunstone to create small space vessels complete with navigation and star-drive capabilities. He once used the ship to take his adoptive father, Jonathan Kent, on a trip to outer space. During their journey, they visited the Kepler Nebula in the constellation of Ophiuchus. Superman allowed Jonathan to pilot the ship on his own for several hours, while he was busy taking care of a Sun-Eater in a neighboring star system. 
In time, the lost Kryptonian city of Kandor was recovered and restored to it's proper dimensions on Earth. Following a controversial period of civil unrest (resulting in the murder of Kandorian leader Zor-El), his wife Alura used Sunstone and reverse-engineered Brainiac technology to uproot Kandor from the planet and place it within a geosynchronous position in opposition to Earth's orbit. This city-planetoid was re-dubbed New Krypton.
On New Krypton, the Kandorians maintained Sunstone processing plants. These plants were once threatened by a stampeding herd of Thought-Beasts, but the Kryptonian Military Guild dispatched the Red Shard unit to herd the beasts away from the critical areas.