The Worlogog is a construct that is part of the cosmology of the Fourth World. Apparently native to Earth the item responds to a person's will and possesses the ability to alter time and space to the wielder's wishes.
The New God Metron used it as part of a machine to transport a group of Justice Leaguers and super villains from Akopolips through several other dimensions to Earth.
It was later manipulated in Zero Hour by the villain Extant to cause disturbances in the Time Stream.
It was later found by Lexcorp's "acquisitions department" in the possession of a Colombian drug baron who was using it as a paperweight. Upon his death, it was stolen by LexCorp and examined by Luthor, dubbing it the "Philosopher's Stone". Since it was resonating in sync with the thought-patterns of an alien in LexCorp's custody, he used it to control the alien in part of a plot against the JLA. However, he soon discovered that the object's power was far greater, however the Justice League defeated him before he could use it.
After experiencing a timeline where, thanks to Superman destroying the Worlogog, Darkseid ruled the galaxy, the Worlogog was returned to Metron.
The Worlogog was eventually turned over to Hourman III of Justice Legion A, in his role as Metron's successor, who would travel to the 20th century. In a bid to grow as a hero by relinquishing some of his power, Hourman concentrated on breaking down the Worlogog, the source of his nigh omnipotence, scattering its components. Part of its power was stolen by Amazo, and the two androids chased each other through time before Hourman regained the Worlogog's full power.
During an undercover mission to locate that source of a new narcotic, the Justice League ELITE encountered a being called Aftermath who was using portals generated by addicts to reach the Source Wall where he believed the Whorlogog was hidden. However, upon reaching where the Worlogog, the item had manifested itself into the image of one of the trapped beings in the wall thanks to the unconscious will of Manchester Black who had managed to insert himself into his sister, Vera Black's, psych. Now named "Eve", Manchester attempted to use her to first rewrite the past to kill Superman and, failing that, destroy London in a bid to break the entire Justice League. Vera managed to regain control and used Eve to restore the city, the lives lost, and the public exhistance of the Justice League ELITE.