Well there's Amiina, the string quartet that tours with Sigur Rós. Quite minimalistic but I love it. Ólafur Arnalds is also great, more classical but it can lean to modern music from times, check out "...And They Have Escaped the Weight of Darkness". Pornopop are also good, but I only have "And The Slow Songs About The Dead ..." Check it out though. For a Minor Reflection are also a great post rock band, they opened for Sigur Rós on their 2008 tour. I only have their first album though.
On the more poppy side there's Sóley, she's lovely. Check out her recent 'We Sink'. Then there's Of Monsters And Men of which you might have heard... Their recent "My Head Is An Animal" is absolutely phenomenal. Also check out FM Belfast's "Don't Want To Sleep", also an amazing album.