In the episode, Desmond Hume (played by Henry Ian Cusick) and Sayid Jarrah (Naveen Andrews) are on their way to the freighter in the helicopter when they hit turbulence, which causes Desmond's 1996 consciousness to take over his 2004 body and switch uncontrollably between 1996 and 2004. In 2004, the helicopter reaches the freighter and Sayid and Desmond are introduced to communications officer George Minkowski (Fisher Stevens), who is "unstuck in time" like Desmond. The writers claim to have been careful not to create a temporal paradox when dealing with time travel, although whether it is possible to avoid paradox in time travel is debatable.
Desmond, Sayid and Frank Lapidus (Jeff Fahey) experience turbulence flying from the island in a helicopter to the freighter 130 kilometres (about 80 miles) offshore. Desmond suddenly flashes back to 1996 when he is serving for the British Army's Royal Scots Regiment. Moments later, when his mind returns to the helicopter, he neither knows where he is nor recognize his companions; he has no memory of his life since 1996. After the helicopter lands, Desmond continues to jump between 1996 and December 2004. Desmond is taken to the sick bay, where Minkowski is tied to a bed because he is experiencing similar problems. Minkowski explains that someone sabotaged the radio room a couple of days ago and that Desmond's ex-girlfriend Penny Widmore (Sonya Walger) has been trying to call the freighter. Sayid uses the satellite phone to contact Jack Shephard (Matthew Fox) on the beach and explains that Desmond appears to have amnesia. Daniel Faraday (Jeremy Davies), a physicist from the freighter, asks Jack if Desmond has recently been exposed to a high level of radiation or electromagnetism. Jack is unsure, and so Daniel speaks to Desmond and asks him about his situation. Desmond responds that he believes that he is in 1996 when he is serving for the Royal Scots. Faraday understands and tells Desmond that he needs to take a train to the physics department of The Queen's College, Oxford University in England to find Daniel the next time that he flashes back to 1996: most saliently, he tells Desmond that he must remember to tell Faraday, back in 1996, to set his electromagnetic device with the numbers 2.342 (23 and 42 being two of The Numbers) oscillating at 11 hertz.
Desmond's flashes become more frequent and longer. In 1996, Desmond tracks down a younger Faraday at Oxford University, who takes Desmond into his laboratory where he is experimenting with a time machine. Setting his electromagnetic device with the new number settings which Desmond has just given him, Daniel places his laboratory rat Eloise in a maze and exposes her to purplish electromagnetic energy. The rat appears to go comatose, then awakens and runs the maze. Daniel becomes excited because he had just built the maze and had not yet taught Eloise how to navigate through it. Desmond realizes that, like the rat, he is caught in a kind of time warp that is toggling his consciousness between two different bodies at two different points in time and space. Eloise dies of a probable brain aneurysm brought on by the exposure to the time lapse. Desmond becomes worried that he will end up like Eloise and Daniel instructs him to find something or someone—a constant—who is present in both times and can serve as an anchor for his mental stability. Desmond decides that Penny can be that constant; however, he must make contact with her in 2004. To find out where she lives, Desmond finds her father Charles (Alan Dale) at an auction buying a journal owned by Tovard Hanso written by a crew member of the 19th century ship called the Black Rock. Widmore gives Desmond Penny's address.
Desmond finds Penny, who is distraught over their break-up and not willing to see him, in 1996. He gets her phone number eventually and tells her not to change it because he will call her on Christmas Eve 2004. In 2004, Sayid, Desmond, and Minkowski escape the sick bay and begin to repair the broken communications equipment. Meanwhile, Minkowski enters into another flash, and suddenly dies. Showing signs of suffering the same fate as Minkowski, Desmond calls Penny. Penny tells Desmond that she has been searching for him for the past three years and they reconcile before the power cuts off. Back on the island, Daniel flips through his journal and discovers a note that he had written, "If anything goes wrong, Desmond Hume will be my constant."
"The Constant" is the second Lost episode to deal directly with the concept of time travel after "Flashes Before Your Eyes" from the third season. While promoting that episode, Lindelof said that it uses the flashback device "in a way we never have before and never will again and while promoting "The Constant", he said that it "upholds that pledge, unpledges it, then repledges it. Lost's writer-producers enjoy science fiction themes such as time travel; however, they were careful not to create a paradox. The ground rules for time-travel in the series are outlined in "Flashes Before Your Eyes"—although, Lindelof has said that "The Constant" is a more important episode in terms of explaining time travel on the show—by Ms. Hawking (Fionnula Flanagan), who explains that certain events are inevitable and the universe will eventually course-correct errors. Had these rules not been established, the writers feared that viewers would lose interest because the stakes of the characters would be lessened. The writers hoped that "The Constant" would further establish that there are no parallel universes or alternate realities. Lindelof reminisced that "just breaking that episode was such a massive headache" and Cuse added that "it was definitely like doing the hardest New York Times crossword puzzle for the week". Whereas the average Lost episode takes two weeks to plan and write, "The Constant" took five because the writers experienced difficulty when determining its effect on future stories. Popular Mechanics analyzed the possibility of time travel using Lost's rules. Michio Kaku claimed that "the show's producers did their homework". According to Kaku, "there's no law of physics preventing this kind of time travel—just a lack of know-how … [but] it would take a very advanced civilization to really do this". Cuse stated that "we [the writers] try to use enough science to give a sense of credibility".
Shooting occurred in the second half of October 2007. The scenes on the freighter in this episode and later episodes were filmed for several days on an actual freighter ten to fifteen minutes offshore the west coast of Oahu, Hawaii, where Lost is filmed. Instead of docking the ship and returning to the middle of the ocean each day, the actors and crew slept on the freighter in parts that were not being used for filming. Some "flashback" filming took place at the Oahu Community Correctional Center. In 1996, Desmond has short hair and no facial hair and in 2004, Desmond sports long and untamed hair with a full beard. Cusick did not cut his hair; it was hidden underneath a short-haired wig by "really talented hair and makeup folks", according to Carlton Cuse. All freighter scenes were shot before Cusick shaved most of his beard for the 1996 scenes. A fake beard was glued onto Cusick for the episodes "Ji Yeon" and "Meet Kevin Johnson" while his beard grew back.
In its original American broadcast, "The Constant" was watched by 12.893 million viewers, ranking Lost eighth in weekly ratings. The episode was watched by a total of 14.998 million viewers, including those who watched within seven days of broadcast, making it the most recorded show of the week; this number went toward the year-end season average. It received 5.4/13 in the key adults 18–49 demographic. The Canadian broadcast was watched by 1.529 million people, making it the sixth most watched show of the week. In the United Kingdom, "The Constant" was watched by 911 000 viewers. 770 000 Australians tuned into Lost, placing it seventy-fifth in the weekly ratings chart.
According to Oscar Dahl of BuddyTV, "lots of people" referred to "The Constant" as "the best Lost episode ever". Bill Keveney of USA Today wrote that it is "arguably the most highly praised episode of [the] well-received fourth season", while his colleague Robert Bianco deemed Henry Ian Cusick worthy of a Primetime Emmy Award nomination. Patrick Day of the Los Angeles Times called the episode a "mind-blowing tour de force". Maureen Ryan of The Chicago Tribune called it a "for-the-ages episode" with "a classic Lost moment" in Desmond and Penny's phone call and "an especially spine-tingling performance" by Cusick. Verne Gay of Newsday raved that "last night's forty-four minutes of Lost were among the most satisfying forty-four minutes in front of the tube in my life." He went on to write that "it wasn't merely a brilliant episode, which pushed the mythology forward more rapidly and richly than any episode in my memory, but it was an emotional release … I actually cried when Penny and Desmond finally … connected" and "there wasn't one, single, solitary false note". Alan Sepinwall of The Star-Ledger said that "it was brilliantly executed, as both a brain-twister and as a love story" with an "outstanding" performance by Jeremy Davies. Jeff Jensen of Entertainment Weekly described the episode as "the best single outing since season 1's 'Walkabout' and named the phone call between Desmond and Penny the best moment of the season excluding any moments from the then yet-to-air season finale. Nikki Stafford of Wizard described "The Constant" as "mindblowing" and cited it as "the reason the hardcore fans love Lost. Matt Roush of TV Guide said that "the time-tripping went into overdrive with this week's brilliant episode … [which] worked beautifully as a showcase for Henry Ian Cusick as the tormented Desmond. It was almost a stand-alone episode, a Twilight Zone/X-Files-style adventure with a start, middle and killer finish.
Kristin Dos Santos of E! "loved every minute" and admitted that "this was one of [her] all-time favorite episodes, what with the undying love business and this indisputable fact: Henry Ian Cusick can frakking act". "The Constant" received high praise from IGN reviewer Chris Carabott calling it "a brilliantly executed hour of television " and "one of the finest episodes in the series". He gave it 10/10, tying it with "Pilot – Part One" and "Through the Looking Glass" as the best reviewed episode of Lost (although no other first or second season episodes, with the exception of the second season finale were reviewed). LTG of Television Without Pity gave the episode an "A+"—the highest grade for any Lost episode. Erin Martell of AOL's TV Squad loved the episode and its unique flashback structure. "The Constant" strengthened her love for Desmond and Penny's story, saying "my heart won't break if none of [Jack, Kate, Sawyer and Juliet] end up together [but] if Desmond and Penny don't reunite, I will be devastated. Oscar Dahl of BuddyTV gave "The Constant" an excellent review, saying that "my mind has never spun this fast after a Lost episode" and the writers have "really outdone themselves" and "do not get enough credit for constantly tinkering with their story structure". Jay Glatfelter of The Huffington Post said that this "episode of Lost not only continued this season's thrilling momentum; it proved to fans that even in its fourth season, it still leaves us with our jaws hanging open … this was the make of possibly one of my favorite Lost episodes ever." Glatfelter also praised the characters, Daniel "more and more becoming one of [his] favorite characters" and calling Desmond "the most intriguing character on Lost [with] the best love story on the show and dare I say on television today". Daniel of TMZ graded the episode as an "A+", considering it to be one of the best Lost episodes. In his review, he compared television to film—specifically "The Constant" to No Country for Old Men, the 2007 Academy Award winner for Best Picture—and decided that television is far superior.
Karla Peterson of The San Diego Union-Tribune wrote that "[I was] almost as touched and relieved by the[ir] reunion as Desmond and Penny are"; however, she did not review "The Constant" as favorably as other critics, giving it an "A–". Dan Compora of SyFy Portal gave "The Constant" a mixed review. He described it as "an entertaining episode [with] a fine acting performance by Henry Ian Cusick", but criticized Desmond's character for his repetetive story arc, criticized Frank's character, saying that "Jeff Fahey is a fine actor, but so far, his character just hasn't really evolved enough for me to care yet" and Compora concluded his analysis with "this episode didn't seem to really raise or answer anything of major importance, so I can't help but feel that it was nothing more than mid-season filler. Ben Rawson-Jones of Digital Spy graded it with four out of five stars, writing that "a refreshing shift in Lost's tone enabled loyal viewers to have their hearts warmed by the long distance smoochfest between Desmond and his beloved Penny".
The episode is currently nominated in the categories of "Outstanding Cinematography For A One Hour Series" and "Outstanding Music Composition For A Series (original Dramatic Score)" for the 60th Primetime Emmy Awards.