The New York three-piece hit the UK with We Are Young – which took the top spot in the singles charts.
Now with another hit, Some Nights, and a top 10 album of the same name under their belts, the band is coming to Scotland for their first headline tour.
But lead-singer Nate Ruess said their success has taken them by surprise.
He said: "It's unexpected for it to have happened the way that it has, based on where we started, how long we've been making music for and where our heads were at.
"Our intention was to just make the best possible album that we could.
"Somewhere early in the process we put down We Are Young and right away our record label had a great feeling about it, which eased the pressure for the rest of it, but the song came with no other intention other than to just be on our album.
"For it to feel so good early on allowed us to make an album that we're proud of. The fact that all this stuff has happened without us trying hard to break into the mainstream has just made it that much better."
Nate started out in the business as a member of indie rock band The Formats, which he formed with school friend Sam Means in 2001.
After splitting in 2008, he contacted Jack Antonoff, of Steel Train, and Andrew Dost, from the band Anathallo, to join his new project Fun. They released debut album Aim and Ignite in 2009.
This gap between it and the release of their current album this year is something which Nate believes helped ground them as a band.
He said: "The main thing with the space between our two albums was just to build on the opportunity for us to become a band that people come and see, at least at first in the US where we began to get a good following.
"We wanted to focus on the live shows and on learning how to be with one another.
"The first album was a real learning experience and with Some Nights it was important that we were close to one another by the time we made it.
"It's tough when you start a band in high school or with the people you grew up with.
"Some people change and grow, and some people who don't during those formative song-writing years.
"I've got nothing against The Format because I am proud of that time, but with this band, I think we are three people, three musicians and three songwriters who have a pretty good idea of who we are and how we could grow together."
Now making an impact in the UK, they are also hob-nobbing with big names in the business, including R&B's songstress, Janelle Monae, who features on, We Are Young.
The collaboration came by chance when their producer Jeff Bhasker, who has worked with the likes of Kanye West, Drake, Jay-Z and Beyonce, ran into her. She was "blown away" by the song and immediately committed to sing.
Nate said: "It means a lot to us because it's Janelle and she is truly an amazing artist.
"It's not just about labels hooking people up, it was purely about the music.
"Her collaboration helped us. We were just so floored to have someone of Janelle's calibre singing on one of our songs."
The music of the band has been described in various ways, from indie to pop to rock, but the term 'fun' is hard to veer away. This might not have been the case if the events of one night hadn't gone quite the way they did.
Nate added: "We were sitting around and trying to come up with the name and someone said 'ice-cream' and I was surprised at the number of people who said 'yeah, ice-cream's a pretty cool name'.
"I was seriously about to walk out and quit the band right there and then.
"But I kind of liked the feeling it conjured up and Jack said 'what about fun?'.
"We spent another six months thinking about it and eventually had no choice but to settle on a name and chose it.
"For the most part we really love it but the only thing we can't stand is people asking us if we're having fun."
l Fun are at Glasgow's ABC O2 Academy on October 8. Tickets are sold out.
Their album Some Nights is out now.