First proposed as a character in November 1938, he didn't actually appear until December 1944. He was intended to be Superman as a boy (later, a teenager). In April 1958, he met and joined the Legion of Super-Heroes -- a group of teenaged superheroes from the 30th century.
In 1984, DC Comics retconned their Superman origins, and eliminated Superboy. The problem was copyright law: In 1976, Congress enacted a new Copyright Act. This law extended existing copyrights for 19 years, but it also gave creators of works the right to seek to recover their copyright when the extension was up. Now, copyright prior to 1976 lasted just for 28 years, although copyright owners could extend this another 28 years if they asked. Superboy's copyright was going to expire in 1994, and it was clear that DC Comics was going to ask for its 19-year extension. Both Jerry Siegel and Joe Shuster indicated they would challenge DC Comics' copyright claim in 1994. DC Comics fully intended to get rid of Superboy and all references to him in their comics in case Shuster and Siegel were successful. The name "Superboy" was generic enough to not be copyrightable (although it could be trademarked, and DC Comics had long done so). But the indicia, the character story, the look of the character, any plot elements or villians which Siegel or Shuster had created? Those were copyrighted. To keep the Legion continuity intact, "Superboy" now become a Superman clone created by the villain known as the Time Trapper. The Legion never went back in time; the Legion was consistently diverted into a "pocket universe" (created by the Time Trapper) which was identical to ours and in which "Superboy" existed.
A year later, a third Superboy was created. DC Comics writers had long complained about the extensive continuity within which they had to work. They wanted all the continuity wiped out, and a blank slate given to them. DC Comics publisher Jeanette Kahn agreed, and in 1985 DC Comics retconned all its heroes. During this "Crisis on Infinite Earths", the idea of a Clark Kent from "our world" (the so-called Earth-Prime) is introduced. Superman journeys to our world, retrieves Clark Kent-Prime, and brings him to the comic book Earth ("Earth-One") -- where he gains his super-powers. He then helps Superman save the universe.
But DC Comics already had a Superboy sitting in the Pocket Universe. It also wasn't clear that Siegel and Shuster would win their copyright claim. DC Comics had to keep the Pocket Universe Superboy due to continuity issues with the Legion, but they didn't need to keep Superboy-Prime. So Superboy-Prime, the aged Earth-2 Superman, the aged Earth-2 Lois Lane, and the Earth-3 Alexander Luther, Jr., are sent into a "paradise dimension".
Joe Shuster died in 1992, and his family signed their copyright interersts over to DC Comics. The agreement barred them from seeking any copyright "clawback" in 1994.
Beginning in 1994, Jerry Siegel sued under the Copyright Act of 1976 to regain his copyright interest in Superboy.
Worried that they could lose the character, DC Comics decided to create a fourth Superboy. Fortuitously, DC Comics had just made the decision to "kill" Superman in a major story line. As part of this story line, several new heroes emerge to claim Superman's mantle, including a robot Superman, a guy in Superman-like armor, and a new Superboy. This new Superboy was a genetically engineered human being whom government scientists named Kon-El. In time, he goes to live with the aged Jonathan and Martha Kent, taking the name Conner Kent (and pretending to be Clark Kent's cousin). Later, it turns out he's really a clone of Lex Luthor and Superman, not "just" a genetically engineered human being. (Even later still, he learns this is false and he's the genetically engineered clone of a scientist... oh, who cares! it's such a goddamn soap opera!) He later dies, but is put in a regeneration chamber and resurrected in the 31st century by the Legion of Super-Heroes.
Conner Kent has had FOUR -- count 'em, FOUR!! -- different looks during his existence. At first, he was a hipster with a leather jacket. That didn't go over very well. Then he was a butch guy in a black t-shirt (his most popular incarnation). He briefly wore a Superman-inspired leotard, and now is wearing a blue-and-red futuristic leotard with stripes down the arms and legs. In none of his incarnations has he worn a cape.
By 2006, DC Comics readers had had enough of the changes made in the "Crisis on Infinite Earths." So had the company's comic book writers, who were sick of recreating the DC Universe. So DC Comics retconned all its comics yet again in a storyline called the "Infinite Crisis". During this storyline, Superboy-Prime has gone insane in the Paradise Dimension. He's come to be extremely jealous of every other Superboy ever made, in whatever dimension, and believes his "birthright" to be Superboy was "stolen" by his placement in paradise. He's also been able to see into other dimensions via some technology he's created, and he is now convinced all superheroes are spineless wimps who cannot really deal with evil. Determined to break back into our world, Superboy-Prime "pounds on the walls of reality" -- creating another "infinite crisis". (This is now a recurring joke among comic book fans.) Once back in the comic book world, he murders a number of villains and commits rape and mayhem. The Earth-2 Superman breaks free from the Paradise Dimension, too, and confronts him -- and is killed by Prime. But by this time, the universe's heroes have banded together to stop him, and Prime is imprisoned on a world with a red sun. Later freed by the Sinestro Corps (the renegade Green Lanterns led by Sinestro), Prime makes armor for himself as part of a new costume. He later joins the Legion of Super-Villains in the 31st century.
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Did I neglect to mention??? One of the replacement Robins (yes, Batman's Robin) is a guy named Tim Drake. Drake is a rich boy who saw Dick Grayson's parents murdered. A master detective, at the age of nine he deduces both Batman and Robin's secret identities. When the second Robin, Jason Todd, is killed by the Joker, Drake takes over as Robin.
In time, Drake leaves Batman's side and becomes a stand-alone superhero, Red Robin.
Red Robin is depicted as having the worst bromance crush in the world on Conner Kent/Kon-El/Superboy. For his part, Conner Kent allows it to occur even though it unnerves him. For years now, fans have pushed for have the two heroes consummate their relationship, but DC Comics won't do it.