“WITH A HYBRID AUDIENCE of young and old rockers, Cheap Trick’s longevity seems assured.” That declaration—made in the January 1980 issue of Trouser Press—turned out to be quite prophetic. But the writer couldn’t have possibly imagined we’d still be talking about Cheap Trick 36 years later.

Yet here we are. And more than four decades later, here’s the band, still putting out records and still touring almost as relentlessly as they did back in 1980. Maybe this can be attributed to Cheap Trick’s humble, hard-working Midwest beginning, which has, for the most part, kept the members grounded. It’s more likely because Cheap Trick wrote perfect, weirdo rock songs that came close to punk rock, but were never too deeply entrenched in any one style.

“We were always wise-asses ourselves, but we never thought we were punk. We were musicians,” says guitarist Rick Nielsen on the phone from his home in Rockford, Illinois, the town that birthed Cheap Trick. “We just did what we did. Some songs were heavy metal. Some songs were punk. Some songs were beautifully written. It was never the same thing over and over and over again. That’s the way we still are.”

Nielsen himself hasn’t changed much, either, a slightly gruffer version of the bug-eyed, ball cap- and sweater-wearing guitar-slinger who became the face of Cheap Trick in the ’70s and ’80s. He’s still a smartass, as evidenced by his response when I tell him that I can’t believe it wasn’t until 1978’s classic live record Cheap Trick at Budokan that listeners finally caught on: “Yeah, really... me, neither.”

By then Cheap Trick had already released three spotless studio albums: their jagged 1977 self-titled debut, the more polished In Color that same year, and Heaven Tonight in 1978. Critics often zeroed in on the band’s image—vocalist Robin Zander and bassist Tom Petersson boasted pinup good looks, while Nielsen was the class clown and drummer Bun E. Carlos looked like he’d been selling insurance for two decades. They received some positive press—Trouser Press Editor Ira Robbins wrote in 1978, pre-Budokan, that “there is no better American band operating today”—and landed tours and shows with bands like KISS, Queen, and Rush. But it was Japan’s embrace, and specifically the live versions of “I Want You to Want Me” and “Surrender” that finally pushed Cheap Trick into the spotlight.

To this day they’re one of rock’s most underappreciated bands—quietly reliable, but known more for their hits than their full body of work. Cheap Trick has remained remarkably consistent over the decades, with a few hiccups—most notably 1988’s pappy blob Lap of Luxury, which spawned the power ballad “The Flame.” That consistency made producers like Todd Rundgren, Roy Thomas Baker (Queen, Hawkwind, the Cars), Steve Albini, and even fifth-Beatle Sir George Martin want to work with the band over the decades.

“We just started pickin’ ’em,” says Carlos during a recent phone chat. “That was probably one of our main pleasures about making records—what cool guy do we get to go in and work with this year?”

Carlos hasn’t toured with Cheap Trick since 2010, but still remains an equal partner with Nielsen, Zander, and Petersson (Nielsen’s son Daxx currently plays drums, including on Cheap Trick’s new record Bang, Zoom, Crazy... Hello). Carlos did, however, recently perform with his old bandmates at the Rock and Roll Hall of Fame ceremony, which Cheap Trick was finally inducted into despite being eligible since 2002. They sounded great, and Carlos was on fire.

“I miss playing the songs. I miss performing with that bunch of guys,” says Carlos, who also released an album this year called Greetings from Bunezuela! “But the way it turned out, do I wanna be on tour with these guys? Nooo thanks.”

Carlos, who also still lives in Rockford, says he occasionally bumps into Nielsen, but they don’t talk much (he and the members were locked in a legal battle for years). If there’s one thing they can all agree on, it’s that they still love the band they formed together back in 1973.

“We have a long history together, and there you go,” Nielsen says. “It’s too bad we didn’t ride off into the sunset together, but that just didn’t happen.”