After Superman died in battle protecting Metropolis, four different heroes appeared each claiming to be Kal-El. One of these was someone who looked like a young, brash teenager, wearing a leather jacket instead of a cape. Revealing himself as a clone of the original Superman, this new hero exhibited similar powers to the Man of Steel, but there were several differences as well. The clone revealed his origins to the media, telling the Daily Planet that when Cadmus director Paul Westfield decided to replace the dead Superman, they attempted to make a clone directly from his genetic material. What he didn't know though is that he wasn't a true Kryptonian clone, as Cadmus kept failing to reproduce the alien DNA, so they combined the Kryptonian DNA with that of a regular human being.
They then recreated the bio-electric aura surrounding Superman's body, with which they were able to replicate some Kryptonian powers, such as a telekinetic field that gave the clone the ability to simulate powers such as flight, invulnerability, and strength, which they called "tactile telekinesis." This new hybrid clone was initially called "Experiment 13" since there were twelve previous attempts at cloning Superman that were unsuccessful. But with attempt thirteen, this new clone was grown into a teenage boy in less than a week, and given implanted memories and originally meant to match the age of the original Superman. But he escaped from his cloning tube early however, entering the world as the equivalent of a teenager.
After Superman came back to life, the clone hero took on the name Superboy, even though he didn't like being referred to as anything other than a man. Superboy moved to Hawaii, where he became the island's #1 Super Hero. He started working as an agent of his creators at Project Cadmus, and was paired with Cadmus' genetic creation known as Dubbilex as his chaperone. He entered into a relationship with TV reporter Tana Moon during this time as well. It was during this era that he learned that he was in fact Cadmus' 13th attempt at creating a Superman clone, and that the human donor of his DNA was Project Cadmus director Paul Westfield. Superboy briefly joined the cosmic heroes known as the Ravers, and also spent some time in the 31st Century with the Legion of Super-Heroes.
Superman formally brought Superboy into the fold when he invited him to his Fortress of Solitude, where he gave him the name Kon-El, making him an official part of his family. He also was given the human name Conner Kent, making him part of his adopted family as well. Superboy also found himself a new group of peers, when he teamed up with other protégé of famous heroes like Robin, Impulse and Wonder Girl in a new team called Young Justice.
The group had many adventures together, but eventually went their separate ways. It wasn't long before they reformed, although they now went by the name the Teen Titans. Another bombshell dropped on Conner's life when he discovered that the human donor of his DNA was not Dr. Westfield, but Superman's arch nemesis Lex Luthor. As Conner matured, so did his feelings for his teammate Wonder Girl. Their romance was cut short however during the INFINITE event, when the extra dimensional Superboy Prime tried to recreate the multiverse. Superboy stopped him, but paid the ultimate price, as he died during the battle.
Post INFINITE CRISIS (2005-2010)
After the universe shattering event known as the INFINITE CRISIS, Superboy was dead and buried. Although many of his fans (and even his girlfriend Wonder Girl) believed he would return from the grave just like Superman once did, a whole year passed, and he remained dead. But in the 31st century, the Legion of Super-Heroes, who counted Superboy as an inspiration, along with his friend Impulse, were able to revive him in the future. He then travelled back in time to the present, resuming his career as Superboy. The newly returned Superboy went to live on the Kent farm at this time, helping Ma Kent fill the hole in her life after the recent passing of her husband Jonathan. He resumed his membership in the Teen Titans, as well as his romantic relationship with Wonder Girl.
The New 52 (2011-2016)
After the DC Universe history is once again rebooted due to events of FLASHPOINT, Superboy reappeared, this time with a new version of the Teen Titans. His entire pre-FLASHPOINT history was erased. This Superboy was still a half-human half-Kryptonian clone, a creation of a shadowy organization called N.O.W.H.E.R.E., who were looking to control a new generation of meta-humans. Despite his conditioning as a weapon, he chose to be a Super-Hero instead, and joined the Teen Titans. When he met Supergirl, he learned of his Kryptonian heritage, but when she discovered he was actually a clone, she gave him the name Kon-El, which translated to "an abomination in the House of El" in Kryptonian.
Kon-El discovered more about his origins, learning that he is actually a clone of Jon Lane Kent, the future son of Clark Kent and Lois Lane, hence the half human/Kryptonian DNA. Kon-El was revealed to have been created by Harvest, the founder of N.O.W.H.E.R.E., so that a cure could be found for the future Jon's illness, which was making him mentally unbalanced and had turned him into a villain. At one point, Superboy is thought to be dead, and the future Jon Lane Kent replaced him in the present timeline.
When the 5th Dimensional Imp Mister Mxyzptlk staged a prolonged physical and emotional attack on Superman, the battle resulted in Superman's timeline changing, and in this new reality, the post-FLASHPOINT version of Superboy and all of his adventures never existed. Whether the original Cadmus version of Superboy will reappear remains to be seen.