Sound advice for anyone touring beyond the English Channel: beware of European (mis)adventure. "We had an especially good time in Brussels last night," says Martin Doherty. "But you know those beers they serve in tiny glasses? You're like 'I'm fine, I've only had four', but you don't realise they're 7%." We're sitting canal side on a bright and breezy afternoon, several hours ahead of a sold out show at Amsterdam's Melkweg, discussing the availability of La Chouffe and various other fine Belgian beverages on tap. The backstage fridge may well be fully stocked with the good stuff, but he sounds a note of caution. "I'm not drinking tonight though 'cos our bus is parked right next to the water - one false move and you're in!"

It seems not even overindulgence or drunken mishaps can halt Chvrches' inexorable rise. The Glaswegian trio have had a stellar year, one of the few bands in recent memory to really deliver on the promise of a couple of brilliant, much-hyped early singles; fifth in the BBC's Sound Of...2013 poll, they were also a minor sensation at SXSW, have toured constantly, and released one of the year's best albums, The Bones of What You Believe. Declared Best New Music by Pitchfork and widely acclaimed in most publications' end of year love fests, it marries glorious hooks to forward-thinking sonics, a dance-floor filler that also nods politely to the indie crowd. It was also, according to multi-instrumentalist Iain Cook, "well on it's way to being finished, with maybe eight or nine songs written" when 'The Mother We Share' exploded across the blogosphere last November.

Perfectly timed to catapult them into Ones to Watch lists, the single created the sort of frenzy and gushing praise normally reserved for returning legends such as David Bowie or My Bloody Valentine. It was also exactly the type of storm that can sink nascent acts before they find their feet, or their voice - just ask Friends or Joe Lean how hard it can be turning noteworthy early material into a career. Weren't they worried about everything spiralling out of control? Apparently not.

"Hype is such a fucking shit word, isn't it?" says Doherty. "It kills people before they get started, but we're really good at blocking that stuff out. We were so busy this time last year that none of us had the chance to stand back and start self-congratulating or whatever, but I'm certainly not daunted by it, because we haven't been paying too much attention. I think that's a more positive way to be, as opposed to enjoying every word written about you, taking it all in, then writing [music] as a reaction or to try and catch that song or moment again. That's a trap we will never fall into."

It also seems they're just as wary of resting on their laurels, as he continues: "As far as I can tell, we've got so much work still to do, so we've been staying as busy as possible, writing songs when we can. Plus learning how to get better live; remember, this was a studio project in the beginning, and now, in the last six months, we've really come a long way in terms of the show, and it's all feeling really good."

It was surprising that Bones didn't appear until late September, an eternity to wait given today's strike-while-the-iron-is-hot PR whirlwinds, but according to Cook, it was all down to logistics and a lack of time. "If there had been no live shows to do during that period, it would've probably been done by last Christmas. But as it happened, we had to go do various bits at SXSW, plus a few other tours here and there." Singer Lauren Mayberry concurs, adding: "We only got signed in the UK in January, which really wasn't that long ago. At the time, it would have been silly for us to try and rush what we were doing; we thought we should take our time to finish the record the way that we would have finished it anyway, and not be pushed into doing things that we weren't happy with. Because at the end of the day, if it goes really well and you made a record you're really proud of that's great, but if it doesn't go that well and you can still stand behind the record..."

Her voice tails off, the thought left unfinished, but it's clear what she means. Chvrches, far from revelling in their newfound fame, have a steely ambition to be so much more than a one-year-wonder. Frustration from years spent grinding away on the indie circuit - Cook in particular recalls one American tour with Aerogramme being especially soul crushing - and gratitude at the opportunities currently presenting themselves have sharpened their keenness to avoid the pitfalls of success, however moderate. "That's a special kind of madness that comes from people who aren't prepared for when things go well," claims Cook. "Or younger people, who are a bit mental anyway; when it happens overnight, they're just not prepared to deal with it or have a support network to help. We've been playing in bands and doing this long enough to...not to be ready, 'cos I guess you never really are ready for when people are suddenly listening to you for the first time..."

"I don't know if I'd use the word 'successful' yet with us either," interrupts Doherty. "I just think that as far as I can see, we have a brilliant chance to be successful at this point - we're working so hard. But all this work has been up to the album, which is just out, so maybe in nine months when we look back we'll be able to say 'Yeah, that was a proper success.' This is why it's important not to listen to what all the people who are making money off you tell you on a day to day basis: 'You are a star, you're a genius, you're special'. That's going to fuck anyone up, hearing that everyday, and the worst thing that could possibly happen is they start taking any of it on board. We all know how that ends."

"It's also important to make sure you work with good people, people you trust to tell you the truth about things good or bad," adds Mayberry. "We have a really small team; manager, tour manager, three crew guys and that's it. Plus, the fact we've had all those [previous] experiences, and been in all those other bands...you don't forget them. So it would be weird to say: 'We're amazing now!' and start acting like assholes. I feel you're a product of your past, and there's no guarantee how long this is going to last."

There never is, but it looks like short term, they have nothing to worry about. It's hard to recall another band touring so extensively and successfully beyond the UK before releasing an album - they've performed 136 concerts across four continents in 2013 - and there's a long way to go yet; after a brief break for Christmas, they head back to Australasia before yet another tour of Europe, this time hitting bigger, grander venues. Six months is a long schedule for any band, but they're not complaining. "It means we've got a job for another six months, so that's brilliant," says Doherty. "This kind of thing is a total privilege, and nobody understands that better than we do. Not until you've slogged it out can you understand how amazing an opportunity this is, and I'm trying to ban complaining on the tour - even myself, like a full ban - because this is going so much better than we could have imagined."

Cook, who knows all about tough times on the road, wholeheartedly agrees. "It means people will be giving a shit about us for the next six months. If things weren't going as well as this, and we were looking at such a full schedule, it would be a different story." Mayberry also notes that it's been good to have an audience that's heard more than just a couple of songs, and to let the material breathe. "Up to recently, it was all pre-emptive stuff to try and get people to hear the band, whereas now we're on an album campaign tour, which is different. We've done a lot, but it's been helpful in my mind to make the band exist in the real world, because it was such an online thing. It's been really good getting out there and showing people that we're real."

Scotland, especially Glasgow, has an incredibly rich musical heritage, from post-punk pioneers Orange Juice to the sweet, soulful indie-pop of Belle & Sebastian. And while the city has always had a vibrant dance scene, the dominant thread running through most successful acts has been a burning desire to mix art pop, disco, and alternative music with six-strings and an amp. I ask why electronic music, and specifically the type of synth-pop that's been so popular over the last few years, has taken a back seat; Doherty's not sure.

"I don't have the answer to that. I think a lot of what happened in Glasgow - certainly as far as my knowledge of what the town was musically, and what I lived through - Chemikal Underground were at the forefront of everything that was going on when I was at school and buying albums, and they signed a lot of guitar-based music, but never a proper synth band. It's an interesting question. What I would say is that when we were forming this band and coming up with ideas, we weren't focussed on what was going on around us. It was coming from somewhere completely different, and just making music that was informed by a) the tiny space we were recording in and b) sounds that were exciting to us. So in a lot of ways, the band isn't really related to Glasgow musically, but we certainly have lived through all that stuff and draw from it."

Unfortunately, it hasn't been all plain sailing, and their growing profile has had some unintended consequences; sexist abuse aimed at Mayberry. After posting a screen grab and complaining about one such vile comment on their Facebook paged, they were inundated with even more, prompting Mayberry to pen an article for the Guardian decrying online misogyny. Predictably - and depressingly - the comments below the line got out of hand, apologists and the ignorant weighing into a debate that has (rightly) grabbed headlines all year. Hitting the national press with such an emotive topic - and perhaps making herself an even bigger target - was a brave move, but something she felt had to be done, a public statement from a prominent figure that such behaviour was completely unacceptable.

Aware it could have led to more problems, she found that "the response has been really positive. When people comment negatively on that stuff, they're just proving the point of the piece, aren't they? We were aware that it would open the channels for abuse wider, for a small amount of time, but I feel like the overall benefit outweighed that. It was nice that we could make a statement on it; I figured we don't really know how long we're going to get to do this, and if it's our 15 minutes, we might as well do something useful while we're here."

It's clearly an issue the band cares about deeply, and nor are they fazed by the usual bleating about musicians mixing art with politics. "It's not like we're standing on a soapbox and talking about politics in general; we're talking about something that's relevant to us on a day to day basis, and I think it's cool to be able to give a sense of what the people in the band are like. What's strange about it is it's not an issue that would marginalise us, because it happens to women all the time. In my mind, its the internet version of honking your horn and cat-calling out a window, so I was surprised by the number of women and men who were in support of it, but then it's a thing that connects to people on a normal day to day level; it's stuff that actually happens. I think it was good, and if some sexist dicks on the Internet don't like me, more to the better."

Our conversation turns to the future, and their plans after this set of commitments is done with. It involves more song writing according to Cook, who adds "I can't wait to get started." "We'll hopefully get back in the studio after this tour," says Doherty. "We'll take stock, sit in the wee old room, make tea, talk shit, and get some ideas down." It transpires that even though Bones is barely off the press, they've already started thinking about and discussing what to do - and where to go - next, evolution rather than revolution being key.

"We've got things we want to try, but I can't imagine going in and completely re-inventing ourselves," says Mayberry. "We'll figure it out once we get in there as we record as we write, and that's the way it's always been. So I can't see us going big box production on our second record, super shiny and polished, because that's not really us." Cook agrees, adding that touring has added another element to their thought process. "Having done so many shows, I think we'll end up writing more songs that we feel are going be good fun to play live. Playing tracks every night, you realise that some bits work really well, and some bits could work better, so that's something we'll have more in mind when we're writing the second album."

Doherty goes one further, and mentions specific ideas he's keen to try. "I want to do something more lean, away from the massive productions kind of thing, and be inspired by people who did it with less; like using one drum sound, one bass sound, one key sound and a vocal, so every single note serves an important purpose. I'd like to experiment with that. Plus we'll just be better [writers], after a years worth of experience. I don't mean it will be a better record - hopefully it will be - but we'll have a clearer idea of what we are creatively, who we are as people, and how we work together. That can only be positive."

As they enthral the packed auditorium later that evening, it's easy to see why they are so effusive about where they are, and where they might end up. Clearer and brighter than on record, the songs pulse and groove, prompting several mass sing-alongs and much dancing down the front. A somewhat flat and uninspired attempt at Whitney Houston's 'It's Not Right But It's OK' shows that they're not immune to the occasional misstep, but it's a minor quibble; the show (and the sound) is utterly brilliant. "It's all been various degrees of highs," replies Cook when asked to sum up their year; it's hard to see that state of affairs changing any time soon.