Top 5 Icelandic music artists (except Sigur Rós and Björk because...well...you can't really top them, now, do you?)

1. Ólafur Arnalds: absolutely my favourite artist right now. He's a very young and very talented composer, who often performs at Harpa and around Europe. His approach to music is fresh and amazing, unlike many young composers nowadays. Seeing him live is an amazing experience. I can't really describe what his music is like: it is true music, you need to close your eyes and listen and nothing else. 
2. Sóley: you probably know her if you listen to Seabear (more about them below). Sóley is a young artist who uses synthesizers and her beautiful voice to create delicate songs which have complex yet enjoyable textures. Her talent live is undiscussed - I actually like her more live than on record. Look for Sóley live at KEXP and see for yourself! 
3. Amiina: again, you probably know them if you know Sigur Rós. They are the supporting band for the most famous icelandic band. They play a weird mix of instruments, from cellos to harps to synthesizers. I always listen to them on my flights to and from Reykjavik (provided there are no drunk danes on the plane - which happens) because you can really feel Iceland's nature in their compositions. 
4. Seabear: amazing music, amazing artwork, amazing people. Pop with a little bit of indie and synths and weird vocals. Love them.
5. Of monsters and men: I know they are now like, world famous or something. But to me, OMAM will always be that new band I listened to at 12 tónar on a rainy day. You may call their music "indie", but it's just so much more: amazing vocals, refrains and textures. Their album "My Head Is An Animal" is a feel good album. And there's so much more about OMAM than Little Talks! 

BONUS TIP: if you love music and are in Reykjavik, you need to pay a visit to 12tónar. I won't spoil anything about it - just go there and enjoy.