"Swindler and con man..."
"Liar and rogue."
"Did I leave you with that impression?"
Mudd claimed that he had been screwed over since the day he was born, and justified his con schemes by claiming he deserved their prizes.
Mudd claimed to have once robbed a Betazoid bank by memorizing all the necessary codes; it was later speculated that in order to have really done this, he would have needed a time crystal like the one he used against the crew of the USS Discovery.
In Mudd's account of events, he fell madly in love with Stella, the only woman he ever loved. Her family did not approve of him, so he felt he had no choice but to try and buy her father's respect. He borrowed a large sum from some non-traditional lenders and gifted her with a moon. This scheme worked, but he eventually fell behind on his payments and his creditors came after him. They chased him into Klingon territory, where he was captured and deposited on a prison ship. (DIS: "Choose Your Pain")
However, when Starfleet researched Mudd, another version of events emerged. They suspected that Stella was merely Mudd's target after they discovered that he had fled her and taken her dowry with him. They theorized that he had fled into Klingon space not to escape his creditors, but to flee her father, who had offered a reward for finding him. (DIS: "Magic to Make the Sanest Man Go Mad")
Captivity by the Klingons
For some time, Mudd shared a cell with Starfleet Lieutenant Ash Tyler. As a method of preventing camaraderie amongst prisoners, when the Klingon guards periodically came to deliver a beating, they would allow the subject to choose one of their fellow prisoners to receive the beating instead. Mudd always chose that option. Mudd kept a pet while imprisoned, a small alien insect-like creature he named Stuart, which he trained to steal small objects such as food, sometimes from fellow prisoners.
In December of 2256, Mudd and Tyler were then joined by the USS Discovery's Captain Gabriel Lorca. After Lorca's interrogation by L'Rell, Mudd was discovered to be spying on his prisonmates for the Klingons, passing on information when other prisoners confided in him. Lorca and Tyler managed to escape soon after, but left Mudd behind. (DIS: "Choose Your Pain")
Escape and reunion with Stella
Escaping from Klingon custody with the help of Stuart, Mudd tracked down Captain Lorca aboard the Discovery in an attempt to steal and sell the ship to pay off his debts with the Klingons, equipped with a time displacement device and traveling inside a gormagander.
With his help, members of the Discovery crew ultimately managed to out-con Mudd, in reuniting him with Stella and her father. Although Mudd already spoke of his love in the past tense, Stella was eager to forgive and marry him, claiming that she had always known what kind of person he was. Her father supported the marriage, justifying this bizarre position by saying he'd do everything for his daughter. Before the duo left with Mudd, Stella's father promised to keep Mudd with Stella, and away from Starfleet. (DIS: "Magic to Make the Sanest Man Go Mad")
Abandoning Stella and life as a con man
Mudd's interstellar exploits began again after he deserted Stella once more, becoming a peripatetic grifter who roamed through the galaxy practicing various cons, schemes, and scams – not always successfully. At some point subsequent to his encounter with Discovery, the Federation had charged Mudd with thirty counts of smuggling, twenty counts of attempted homicide, one count of attempted regicide, and "penetrating a space whale" (the aforementioned gormagander), and offered a bounty of 100,000 credits for his capture. In typical fashion, Mudd turned this to his advantage; he built or obtained a number of android duplicates of himself, and (while disguised as a female alien bounty hunter) sold these androids to other bounty hunters, whose hopes of receiving the bounty on the real Harry Mudd were dashed upon discovering that they had paid for an android copy. (ST: "The Escape Artist")
By 2266, Mudd had been convicted of smuggling (receiving a suspended sentence), transporting stolen goods, and purchasing a space vessel using counterfeit currency. For these last two crimes, Mudd was sentenced to undergo psychiatric treatment, the effectiveness of which was officially disputed. He held a Master's License, permitting him to legally operate a spacecraft, but this license was revoked on stardate 1116.4 for operating stolen spacecraft and transporting illegal goods. (TOS: "Mudd's Women")
First encounter with the Enterprise
Mudd was first encountered by the crew of the USS Enterprise in 2266. Mudd, using the illegal Venus drug, attempted to sell Eve McHuron, Ruth Bonaventure, and Magda Kovacs to a group of lithium miners led by Ben Childress on Rigel XII. The drug gave the impression that the three women were beautiful, when in fact they were not. Childress and the other miners married the women anyway, as they were more interested in companionship and the benefits that having three practical, intelligent women around could provide, and the women were happy to escape their previously lonely existence. Before leaving Rigel XII, Mudd asked Captain James T. Kirk if he could remain on the planet, saying it would be adequate punishment, though this request wasn't granted. Criminal charges were later pressed against Mudd for his actions and he spent at least some time in jail. (TOS: "Mudd's Women")
Hot water on Deneb V
Somehow, though, Mudd soon escaped. He then promptly began to sell the plans for alien technologies to various worlds – without bothering to pay any royalties to the actual off-world patent holders. This ended when an attempt to sell Vulcan fuel synthesizer technology to the inhabitants of Deneb V backfired. The transaction was unmasked as a hoax when the Denebians actually contacted Vulcan to ensure that Mudd had the rights to sell the technology in question, which, of course, he did not. (TOS: "I, Mudd")
Second encounter with the Enterprise
The penalty for fraud on Deneb V was death. However, Mudd managed to "borrow" a spaceship and escape before the sentence could be carried out. He ended up fleeing to a previously uncharted planet, one that was populated entirely by androids programmed to adapt the planet for productive use, who became interested in studying Mudd as a specimen of Humanity. This meant that while the androids attended to his every need, and even made him the titular ruler of the planet (later named Mudd in his honor), Mudd was not allowed to leave.
Mudd then attempted to broker a deal where he would be allowed to escape if he provided the androids with other prime Human specimens to study. Therefore, in 2268, Mudd identified the starship Enterprise to the androids as a likely source of exceptional examples of Humanity. (Mudd had no idea at the time that the androids instead planned to take over the galaxy and make all organic sapient races so totally dependent on them that they could effectively enslave these races.) Subsequently the android known as Norman, posing as a member of the Enterprise crew, successfully took control of the ship and took it to the planet Mudd. The crew of the Enterprise, however, was able to escape captivity by identifying Norman as the control for all of the planet's androids. The crew proceeded to confuse Norman with illogical behavior, causing him to break down. After the androids were reprogrammed, Mudd was left behind on the planet as an example of a Human failure – along with five hundred uncontrollable android replicas of his shrill wife Stella for company. (TOS: "I, Mudd")
Third encounter with the Enterprise
Eventually, Harry Mudd stole another spaceship and escaped the androids' planet in 2269. He traveled to the planet Ilyra VI and "sold" Starfleet Academy to its inhabitants. Mudd then used the proceeds of that con to travel to Sirius IX, where he discovered a love potion crystal that he sold to over a thousand of the planet's inhabitants. Unfortunately, the buyers suffered allergic reactions to the crystals, and Mudd was forced to flee to the mining planet Motherlode, where he also tried to sell the love potion drug. Once again, however, he encountered the crew of the Enterprise and was captured by Captain Kirk and Spock.
Mudd was incarcerated in the brig, where he gave the love potion to Nurse Chapel as a gift. She then took the potion to Spock, but found that it did not take effect immediately; as a Vulcan, the effects of the drug took longer. Later, the drug did affect him, and Spock fell in love with Chapel. Fortunately, the drug only had temporary main effects – and a rebound aftereffect. After yet another escape, Harry Mudd was again captured and sentenced to an indefinite period of rehabilitation therapy, without guarantee that it would be effective. (TAS: "Mudd's Passion")
"Who are you?"
"The name is Mudd. Harcourt Fenton Mudd, Harry for short. I reiterate – ouch."
- - Harry Mudd and Gabriel Lorca, after the latter grabs the former's neck upon awakening (DIS: "Choose Your Pain")
"You can't walk away from me, Lorca. I'm coming for you. You hear? You haven't seen the last of Harcourt Fenton Mudd!"
"But men will always be men no matter where they are."
"You see, gentlemen, behind every great man there is a woman urging him on. And so it was with my Stella. She urged me on into outer space. Not that she meant to, but with her continual, eternal, confounded nagging. Well, I think of her constantly, and every time I do, I go further out into space."
- - Harry Mudd, describing his antagonistic relationship with Stella, and then being trapped with five hundred copies of his nagging wife (TOS: "I, Mudd")
Harcourt Fenton Mudd was performed by actor Roger C. Carmel in the three episodes he appeared in for TOS and TAS. With the exception of the Enterprise crewmembers, Mudd was the only character to be played by the same actor in more than one episode of Star Trek: The Original Series. He was later played by Rainn Wilson for his appearances in DIS and ST.
The character of Harry Mudd, as devised by writer Stephen Kandel, was inspired by the fact that NBC had announced fears that the first Star Trek pilot episode, "The Cage" (with its alien Talosians), would not be understood by its audience. Kandel later recounted, "I said, 'What if we start with a character who isn't alien or highly technologized, but rather somebody with whom the audience would easily identify?' What we came up with was a roofing salesman, a con man." (Starlog issue #117, p. 44) Kandel also stated, "I originally had the idea of a kind of a traveling salesman and con man – the medicine salesman in The Wizard of Oz, that ends up as the Wizard, an interstellar con man hustling whatever he can hustle; a lighthearted, cheerful, song-and-dance man version of a pimp."
Stephen Kandel was given the chance to develop one of Gene Roddenberry's story outlines, "The Women", which was basically about "space hookers" bound to be sold as wives on a distant planet by an "intergalactic pimp", named "Harry Patton". Kandel felt the story lacked a focal point character, and merged it with his idea of the charismatic con man. (These Are the Voyages: TOS Season One, pp. 43 & 133)
In a revised draft of the story outline for "Mudd's Women" (dated 23 July 1964), Mudd was described as "an old reprobate named Harry Mudd who has a colorful reputation in space for fly-by-night schemes, grandiose promotions, and suspected smuggling. And yet it is impossible not to like Mudd."
In the final draft script of "Mudd's Women" (dated 26 May 1966), Mudd was initially described thus; "HARCOURT FENTON MUDD... Harry Mudd... scoundrel... delight... conniver... hustler... and much, much more... half the classic Scaramouche... half the classic almost everything else. Harry Mudd, in a word, is style... and all his own kind." Later in the script, Mudd was referred to as having a "razzle dazzle, extra-legal kind of approach to life," and the teleplay continued, "His instinct is to scratch, scramble and con... his nature is precisely what he says it is and nobody believes."
According to the "Mudd's Women" final draft script, Mudd was born on Antares Pi Four and was forty-seven years old at the time of the episode.  This would place his birth at about 2219, making him the same age as Doctor Richard Daystrom.
Stephen Kandel was highly proud of having conceived Harry Mudd. "Harry Mudd was a marvelous character because of the highly recognizable Human quality set against the alien-in-time or alien-in-space activity that evolved," Kandel remarked. "That's what made it amusing, and it's also hard to do because you had stern-jawed Kirk who would meet an eight-foot intelligent reptile and deal with him as any astronaut would. Then, the reptile would meet Harry Mudd, whose first impulse would be to run and hide, and second impulse would be to sell it scale enhancer." (Starlog issue #117, p. 44)
Stephen Kandel was also impressed with Roger C. Carmel's performances of the role, enthusing, "Roger C. Carmel was wonderful as Harry. He inhabited the character and expanded it [....] He developed the character physically as an actor [....] He WAS the character to such a large degree that no one else could possibly play the part." (Starlog issue #117, p. 44) "It was an ideal part for him," Kandel also commented, and related that he believed the role fit Carmel to such a degree that the actor was slightly frustrated that the other roles of his career failed to measure up to it. (The Star Trek Interview Book, p. 134)
Along with Khan Noonien Singh, Mudd was one of only two opponents to face Kirk more than once in live-action Star Trek productions. Mark A. Altman observed that the repeated appearances of Mudd served as a precedent for crossover appearances later in the history of Star Trek, such as the initially TNG characters of Q and the Duras sisters reappearing on Star Trek: Deep Space Nine. (Trek: Deepspace Nine, p. 70)
The Art of Star Trek contained a photo of a raktajino bottle from Quark's Bar which bore a label stating: "100% Colombian," "Made from the Green Hills of Earth" (a title of a short story by Robert Heinlein), and "Imported by Harcourt Mudd." If this was canonical and referred to the same Harcourt Mudd, it would indicate that Mudd entered into this business sometime after the First Khitomer Accords and his original misadventures with the crew of the Enterprise, because raktajino was unknown to the Federation in the 2260s, as documented in DS9: "Trials and Tribble-ations".
During pre-production on DS9: "One Little Ship", Ira Steven Behr voiced regret that the episode's villain wasn't "someone like Harry Mudd." Behr went on to say, "He's a real villain, but essentially a comic character, and that would make the two sides of the story match up." Because it was too late in the process of the episode's creation for such a drastic change, however, the concept of using Mudd was largely forgotten by the DS9 writing staff. The only exception was in the mind of Hans Beimler, who imagined an ending to "One Little Ship" if Mudd had indeed appeared therein. Relaying the conclusion, René Echevarria said, "Once Harry realizes he's been foiled, he steals a runabout and tries to make his escape from the Defiant [...] He gets pulled into the [episode's] anomaly and it's about to close up forever when we beam him onto the ship, and he's only [a fraction of an inch in size] [...] And Odo says, 'Well, at least we won't have to feed him very much!'" (Star Trek: Deep Space Nine Companion, p. 531)
Before actor Greg Grunberg portrayed Commander Finnegan in Star Trek Beyond, multiple individuals suggested to him that he should play Harry Mudd in the alternate reality films. "I would absolutely love to play Harry Mudd, that would be incredible," Grunberg enthused. "I would have to redefine the character and do it the way I see doing it, but that character to me has comedy and brings levity and I would be able to work with robotic chicks. How fun would that be?" Regarding Mudd's appearance, Grunberg reckoned, laughing, "I would go with the big mustache and an earring, why not?" 
The casting of Rainn Wilson as Mudd followed a general meeting he had with the newly formed DIS writing staff, the actor having asked his agents, as soon as he had heard about the new series, if they could set up the meeting. During the conversation, he remarked to the DIS staffers that he would "love it" if there was a role in the series for him to play. Although the writing staffers were unsure if there was anything suitable yet, they promised to keep him in mind.  "We said, 'Well, we'll keep in touch,'" continued Executive Producer/Writer Aaron Harberts. "He left, and we got into thinking about these little Easter eggs and someone said, 'Oh, Harry Mudd has to make an appearance.' That's when we said, 'Oh my God, that's Rainn.'"  Approximately six months after the initial meeting, Wilson received a phone call asking him if he would like to portray Mudd, an offer he enthusiastically accepted. 
In adopting the Mudd role for DIS, Rainn Wilson was pleased with the amount of creative leeway he was given with the part. "I got to take what Roger Carmel did with the original character and then add my own, special sauce," Wilson commented. "He created a fantastic, flamboyant, over-the-top, mischievous but kind of dangerous character. I get to bring a little more to it." (Star Trek Magazine Discovery Collectors Edition, p. 40) He also stated, "To get to go back and do a classic character from TOS... [....] It really was a dream come true for me." One of the factors Rainn "really loved" about Mudd was that he had a backstory which preceded even his earliest appearances in DIS. However, Wilson was also of the opinion that his presentment of the Mudd character was in sync with how Carmel had previously played the role. "He was always deadly. Remember, in 'I, Mudd,' he's going to trap them on a planet with androids and take the ship and leave them to die. Mudd has always had a dark edge. He's a con-man and a merchant and a trickster, but he's always had a deadly edge. So, I think they're continuing in that tradition." 
Mudd's outfit in "Choose Your Pain" was designed by Gersha Phillips, mostly cut from leather, and fabricated by the show's costume department. The outfit was inspired by the stage costumes worn by English musician Adam Ant. After being used in the series, it was displayed as part of an exhibition at San Diego Comic-Con in 2017. (Star Trek Magazine Discovery Collectors Edition, p. 41)
Ultimately, Aaron Harberts and the rest of the creative team have been pleased with the depictions of Mudd in DIS. Harberts consequently referred to the character as a "huge throwback, but one that reaped huge dividends." 
In the video game Star Trek: 25th Anniversary, Mudd encountered Kirk again in 2268, between the events of "I, Mudd" and "Mudd's Passion". He was discovered on a salvage mission of a derelict ship of unknown alien origin. While aboard, he managed to accidentally sell weapon components to pirates, become infected with unknown alien drugs, nearly kill an Enterprise landing party with faulty equipment, and destroy a priceless archive of computer records. Following the conclusion of his investigation, Captain Kirk ordered Mudd to donate five of every artifact he found to research. Also, Lt. Uhura arranged for Mudd to meet his "long-lost wife" at a nearby starbase. In the game, Mudd's voice was provided by Tom Wyner.
In US comic strip "It's a Living", Mudd later purchased a planet for its rare ores, but found, to his dismay, that the planet was actually a large egg for a space-faring creature. After it hatched, Mudd sold the planet back to its original owner (who was unaware of the creature), but he still ended up losing out, as the ores were then floating in space and were actually easier to mine.
Other appearances of Mudd include Where Sea Meets Sky, Mudd in Your Eye, "The Business, As Usual, During Altercations" (from Mudd's Angels), "The Light Fantastic", "Operation Con Game", "When You Wish Upon a Star...!", "Mudd's Magic!", "Mission: Muddled", "The Sky Above... The Mudd Below", "Target: Mudd!", "Made Out of Mudd", and "The Survival Equation".
Harry Mudd's mirror universe counterpart appears in issues 1 and 2 of the comic series Star Trek: Discovery - Succession. He is known to be more of a humanitarian concerned with helping the refugees of Risa, although he has a prior relationship with the mirror universe counterpart of Michael Burnham. He has also smuggled weapons in the past, indicating a shady background.
Harry Mudd's alternate reality mirror universe counterpart appears in the fiftieth and fifty-first issues of the Star Trek: Ongoing comic series, where he has been doing business with the mirror universe counterpart of James T. Kirk on the planet Arronia II. When he attempts to re-negotiate his terms with mirror Kirk, the deposed captain shoots and kills Mudd and leaves the planet on his ship.