"I love the Barrowland. It was a big deal for us playing there, as we'd always been told we were this Southern nancy band and our music would never travel," recalls Mat Osman, the band's bassist.
"The Barrowland just has this reputation that, if you're good it'll be the gig of the tour, and if you're bad - God help you.
"Some of my favourite gigs were there, there's a reason that we've played there more than any venue outside London and it's the first place on the tour sheet.
"People love music in Glasgow, and they're so physical about it. There's nothing worse than a gig where people are clapping, I want them throwing themselves around a bit."
The group are back at the venue this Sunday, promoting their first album in 11 years, Bloodsports.
Coming three years after they first reunited, it's proved an unexpected hit, standing up to the best records in the band's past and suggesting that Suede are still as relevant today as in their 90s heyday.
For Mat, who's been in the band from the very beginning, live shows are key to the group.
"I think people have a very strange view of us and think we're fey Southerners weeping into our fringes, but we've always been pretty fierce live," he argues.
"When we got back together we saw a couple of reformed bands and they'd be playing with orchestras - it was very slick.
"People were going there just to say they'd seen them, so we stripped everything back - there's no tapes or samples or backing musicians.
"We went back to the early days of just making a racket."
There is a key difference from those early days, of course, as guitarist Bernard Butler is no longer in the group, and it's the latter-era Suede that are back together, with Richard Oakes as guitarist.
By the time Oakes joined in 1994, the group had already transformed British music, their 1993 debut shaking up a stale scene that was more focused on American talent than homegrown music.
The second album, Dog Man Star continued the group's success while also helping usher in Britpop, something the band now regret.
I look back on Britpop now, and I hate it - it was nationalistic, which I hated, and all beery and macho," says Mat.
"We weren't a celebration of Britishness, we were a condemnation of it.
"That football image of Britpop, that's not us at all.
"In terms of showing that young, independent bands could make hit records, it was a great thing.
"It was almost the last hurrah of working class bands, but in terms of the drunken cartoon it became it was horrible."
Britpop's aftermath saw many a band disappear, and the same was true of Suede, who broke-up in 2003. Yet reunion gigs in 2010 were a hit, and thoughts soon turned to a new album.
Making Bloodsports wasn't easy, however.
"We started thinking about an album early on, but it's seductive doing live gigs, because we get to play the best songs of a 20 year career to a bunch of people who haven't seen you in 10 years," explains Mat.
"So you go 'wow, everyone loves that, we'll make a record like that' [the hits], and then you realise there's a reason why it took 15 years to make the songs.
"I think that's why so many bands who come back either don't make a record or make a rubbish one. It's not like riding a bike, you have to go back and start from scratch again .
"We threw away 30 or 40 songs, we had an album almost finished and then changed our minds about it - there were points where we thought this wasn't going to work, we don't have it in us."
The resulting record is a triumph, however, crammed with energetic, lusty guitar pop. It's also got eccentricity to it, something Mat believes all good pop should possess.
"It doesn't matter whether it's guitar bands or kids with samplers, what's important is just whether it had this eccentricity that British music always had," he says.
"Britain's always taken the most unlikely people and made them pop stars, your John Lydons, your Bobby Gillespies, your Marc Bolans - these are people that no talent show would ever let get into the second round.
"The irony of the X Factor is that the one thing it crushes out of contestants is that oddity."
l Suede, Barrowland, Sunday, sold out, 7pm