By Gillian Telling
Updated May 11, 2015 at 08:15 PM EDT
Credit: Jeffrey R. Staab/CBS via Getty Images

Dave Grohl and David Letterman go way back—two decades, in fact, when Grohl’s band the Foo Fighters made their first appearance on Late Night in 1995. Since then, they’ve played the show countless times, and Letterman, who is an admitted huge fan of theirs, even requested that they be the first band to play his return show following heart surgery. “‘Everlong’ was apparently his favorite song,” Grohl tells EW. “We dropped everything to do it. I think we canceled a tour. It was an honor to be asked.”

But Letterman was more than someone the band admired and liked playing for—he was also an influence in their formative years, and later, in their careers.

“I grew up watching him as a teenager in Springfield, VA,” Grohl says. “I would stay up every night to see him and his band. I was an aspiring rock musician, and the Late Night band in the ‘80s was the best rock and roll band on television. Their drummer, Steve Jordan, was a huge influence on me. I love Letterman—his wit, and sarcasm. I related to him. So we were obligated to play that show, not just because he’s been a huge part in the career of our band, but our teenage years.”

As the Foo Fighters continued to play for Letterman over the years, their bond strengthened. “I think we mean a lot to each other,” he says of their mutual admiration. “We’ve traded cigars, I’ve given him guitars and snare drums. We gave him a guitar once as a thank you, and he got really emotional with us. It clearly meant a lot to him. He’s just genuinely a warm, sweet person.”

One of the most poignant interactions between the Foos and Letterman occured recently, when Letterman told them why their song “Miracle” meant so much to him. The clip ended up going viral online. “It was crazy,” Grohl says. “He personally requested that we perform ‘Miracle’ after the show was over, and comes out and tells this story. We didn’t know anything about it. We had no idea how important the song was to him. So we’re standing there listening, and just holding back tears.”

Now that Letterman is retiring on May 20, Grohl says he’s going to be hard to replace—especially when it comes to the host’s influence on music. “He always had cutting-edge artists, more so than anyone else,” Grohl says. “It’s really important that people in his position understand that they have influence over the direction of pop culture. I remember seeing The Pixies on his show, and bands you wouldn’t see anywhere else. He was always the place to go to discover something new. There’s something rock and roll about Letterman. He’s shaped generations of people.”

So, he’s going to miss him, then?

“We’ve done a lot of those TV shows,” Grohl admits. “But nobody has the heart that Letterman has. Not even close.”