Unlike most of the central Muppets characters, Gonzo is not a puppet version of a human or a recognizable animal. He sports a bizarre, non animal-like appearance, which includes purple-blue fur, purple feathers on his head, bug-eyes, and a long, hooked nose. In The Muppet Show he performed as a performance artist, stunt double and daredevil under the name "The Great Gonzo."
In the first season of The Muppet Show, the character had sad and immobile eyes. The producers noticed that he worked better in a more energetic form and modified the eyes to have movable eyelids which helped make him a more active character. As such, he became one of the principal characters in the series. Gonzo is known for his wild-eyed, optimistic attitude, yet he is also something of an intellectual. In his revised incarnation, Gonzo, rather than feeling misunderstood by the audience, was dedicated to performing for its own sake, regardless of audience reaction. In one episode, after Kermit decides to cancel a jousting sketch, Gonzo, in armor for the sketch, forces Kermit, at lance-point, to reverse the decision. Floyd Pepper, also in armor for the sketch, observes the exchange with amusement, then asks Gonzo, regarding the sketch, "Do you really think this will work?" Gonzo replies "No! Isn't it terrific?!" Several of Gonzo's stunts have often gone wrong or do actually work in wrong ways. One notable stunt involves him catapulting himself into the balcony box of Statler & Waldorf, but the catapult broke down and in his attempt to fix it, Kermit and Miss Piggy are sent flying instead, Gonzo claiming that they stole his act. Statler and Waldorf have actually been victim to several of Gonzo's stunts including a motorcycle stunt in which Gonzo intends to drive a motorcycle off a ramp into the box of the hecklers (who are chained to their seats by Gonzo). Although the stunt works, Gonzo loses control of his bike and crashes it into the box, knocking the men unconscious. It is plausibly arguable that Gonzo's penchant for death-defying acts came from a Muppet Character Shop idea for a spoof (essentially a Muppet version) of Evel Knievel.
A running gag related to Gonzo is that it is not clear what species he is supposed to be. John Cleese, in his appearance on the show, referred to him as "the ugly, disgusting little one who catches cannonballs". In The Muppet Movie, Kermit, while having his inner conversation, says "And a thing, whatever Gonzo is. He's a little like a turkey," to which his inner self replied "Yeah, a little like a turkey, but not much."
In the film The Great Muppet Caper, he is shipped to England in a crate labeled "Whatever" (while Kermit the Frog and Fozzie Bear are respectively labeled "Frog" and "Bear"). In the Muppet Treasure Island CD-ROM Game, Gonzo and Rizzo the Rat land in a bucket of molasses, following the dialogue of a carriage driver saying "It's raining rats and... whatevers".
In Muppets from Space, it is revealed that Gonzo is an alien and his alien family comes to Earth with a big party for him and before their departure they ask him to return to space with them. Gonzo sadly says farewell to The Muppets but he soon realizes that he would be abandoning his longtime friends who have been like his family all along and declines the Aliens' offer.