Pop-punk is designed not to affront listeners but to gratify them. Illustration by Erik Carter

In 1988, the Los Angeles punk band NOFX celebrated its fifth birthday by embarking on a tour of Europe. The first engagement was in Rotterdam, in front of hundreds of people, virtually all of whom were unimpressed. “I thought you guys were a lot better,” the promoter said after the show. Mike Burkett, known as Fat Mike, is the bassist and lead singer of the band, and in a new oral history called “NOFX: The Hepatitis Bathtub and Other Stories,” he explains that the rest of the tour substantiated the promoter’s judgment. “It finally started to sink in that maybe we were not a good band,” he recalls. Audience members hurled insults, or bottles. Burkett was ready to quit when a friend played him a brilliant new album of “melodic punk rock” by a more established band, Bad Religion, which gave him a better idea. He writes, “I had a new plan: stop sucking.”

This was not easily done. Musicologists may dispute, even now, that it was ever really done at all. But, in the years after that European tour, NOFX honed a slaphappy version of punk rock, fast but surprisingly catchy, with Burkett delivering his sneering lyrics more or less in tune. Mediocrity remained central to the NOFX brand: the band’s two live albums are called “I Heard They Suck Live!!” and “They’ve Actually Gotten Worse Live!” But, starting in the nineteen-nineties, NOFX put out a series of spirited and memorable albums, which sound even more impressive once you read about the trying conditions under which they were created. “The Hepatitis Bathtub” is nominally a story about a band that somehow failed to fail, but it is also an estimable work of anthropology, criminology, and, above all, pharmacology. NOFX never broke up, and even without the benefit of a hit the band has amassed fans all over the world, enough to launch “The Hepatitis Bathtub” onto the Times best-seller list, at No. 3, in a category that surely amused Burkett and his bandmates: “Celebrities.”

Years after Burkett hatched his plan, he helped encourage the next generation of punks to think big. In suburban San Diego, a NOFX fan named Tom DeLonge was inspired by the group’s 1994 breakthrough album, “Punk in Drublic.” The album opens with a rousing two-minute blast called “Linoleum,” which is enhanced by deft tempo changes and some fairly precise vocal harmonies. In a 2014 interview, DeLonge remembered how impressed he was. “It was game-changing,” he said. “It sounded good.” He began to wonder whether it might be possible for his own band to evolve, too.

His band was called Blink-182, and he had formed it with his friend Mark Hoppus, who shared his obsession with punk—and, in particular, with pop-punk, a seeming oxymoron that was in fact a subgenre, known for simple chord progressions and memorable tunes. Pop-punk is user-friendly, designed not to affront listeners but to gratify them; some traditionalist punks consider it at best a guilty pleasure and at worst an abomination. But DeLonge and Hoppus played their four-chord songs with guileless enthusiasm, and their lovesick lyrics mimicked plot points from clean-scrubbed teen movies. They had a surprise hit in 1997, when rock radio stations started playing “Dammit,” which has a refrain that speaks for wistful high-schoolers (and former high-schoolers) everywhere: “I guess this is growing up.”

Instead of shrinking from mainstream success, the band embraced it. DeLonge and Hoppus fired their original drummer and hired Travis Barker, who is (unlike either of them) a virtuoso; in 1999, the trio released an album called “Enema of the State,” which eventually sold more than four million copies in the United States. In the video for “All the Small Things,” they dressed up as members of an unusually inept boy band, but as the song ascended the pop chart, eventually reaching No. 6, the parody began to seem like a prophecy. They more or less looked the part—one early review in Billboard flagged their “beach-boy good looks.” And their commitment to juvenile humor (the stage banter on their live album can be summed up in two words: “dog semen”) camouflaged an equal interest in the evergreen pop topic of adolescent melancholy. At the center of “Enema of the State” sits “Adam’s Song,” a plainspoken chronicle of depression, with a video that became an MTV staple. They were pop-punk pop stars, and they cannily found ways to shift their focus without unduly complexifying their music.

Their adolescent outlook, especially in the early years, occasionally found expression in spiteful breakup songs in which boys wonder what’s wrong with girls. “Enema of the State” included “Dumpweed,” a downright giddy farewell to a “nightmare” girlfriend, in which DeLonge sings, “I need a girl that I can train.” But many of Blink’s best songs endure because they turn inward: the lovelorn boy has sense enough to wonder what’s wrong with him.

“Take Off Your Pants and Jacket,” from 2001, is by turns peppy, sulky, and stupid—Blink-182 at its finest. And in 2003 the band released a moody untitled album that became an unlikely fan favorite. Listeners who had once thrilled to a composition called “Dick Lips” were now just as happy to sway along with “I Miss You,” a subdued love song that had Hoppus murmuring the first verse and DeLonge yelping the second one, which sounded like “Where arrre yehw? / And oy’m so sah-ree.” DeLonge is known for his unplaceable drawl (SoCal skateboarder, perhaps, with a dash of London punk, in a combination so distorting that it can resemble a speech impediment), and its persistence reassured fans that he still hadn’t finished growing up, and perhaps had barely started.

By 2003, when the untitled album came out, Blink-inspired acts like Avril Lavigne and Good Charlotte were beginning to appear, proffering their own combinations of punk and pop, and supplying a guitar-driven alternative to the R. & B.-inflected hits of Britney Spears and Justin Timberlake. (Compared with the sexually suggestive, sonically adventurous teen idols who ruled MTV, these young punks could seem charmingly square, with their unsyncopated rhythms and just-be-yourself attitude.) Blink-182 did not invent pop-punk: a bratty, sappy California band called the Descendents essentially created the style, in the early nineteen-eighties, with a sublime little album called “Milo Goes to College.” And Green Day, a decade later, was the first truly mainstream pop-punk band. But it was Blink-182 that emerged as a touchstone, spawning more imitators than any American rock band since Nirvana. Their seeming ordinariness convinced a generation of goofy punks that maybe they, too, could turn out deceptively simple songs as well constructed as anything on the pop chart. And their prankish camaraderie made fans feel like members of their extended social circle. In a 2002 documentary, Hoppus grew earnest while talking about DeLonge. “He’s my best friend,” Hoppus said. “I’m sure he’ll always be my best friend.”

In recent years, Hoppus has had occasion to rethink that “always.” (Perhaps this, too, is growing up.) In 2005, the band announced an “indefinite hiatus,” apparently at the insistence of DeLonge, and then reunited a few years later and created an album called “Neighborhoods,” which was decidedly ungoofy but surprisingly effective. Then DeLonge stepped away again—he is currently working on a multimedia project inspired by his research into exoplanetary life—and Hoppus and Barker decided to do something radical: hire a replacement. The new guy in Blink-182 is Matt Skiba, a singer and guitarist who is part of the Blink generation—the founder of an excellent goth-inflected pop-punk band called Alkaline Trio, which built its fan base in the aughts. Skiba, because he has a track record of his own, is obliged to sing like himself: apparently he is the rare Blink-182 fan who doesn’t do an impression of DeLonge’s accent, at least not when he is near a microphone. A few weeks ago, during a private concert in New York, sponsored by Spotify, Skiba sang DeLonge’s part in “First Date,” an old standard, snarling instead of drawling. The fans chanted, “Ski! Ba! Ski! Ba!”—a gesture of welcome.