The first and most prevelant form of Kryptonite mythos is the green variety, definitely the most famous and deadly of them all. Superboy first encountered it as a lad, nearly snuffing out his young life before his step-parents removed the harmful element from their home. Although Kryptonite appeared earlier on Earth-Two chronologically speaking, in the jewel of a crook known as Swami Riva, that Superman was an adult when he first ecountered it unlike his Earth-One twin. When each visited the others universe, they learned that this element effects them the same even if not from their native universe. Thankfully, they always managed to outsmart foes who used it against them.
At one point, after the explosion of a nuclear reactor all the Kryptonite on Earth-One was rendered inert leaving the Man of Steel invincible, that is until more of this element arrive on his planet from space. Earth-Two never seemed to have as much of this radioactive rock land on its surface, although its Man of Steel had other weaknesses unaccounted for by his counterpart, hence both Men of Tomorrow had to face their fears repeatedly and show why they were Super men!