While focusing heavily on learning Icelandic, I dug deeply looking for Icelandic-language music. There are surprisingly high amounts of Icelandic bands that sing exclusively in English. Here are my favourite songs with Icelandic lyrics:
Mammút - They play energetic rock music, bordering on post-punk sometimes. The first Icelandic language band I liked, and my favourite still. Here’s Svefnsýkt: <iframe width="420" height="315" src="http://www.youtube.com/embed/aeGZriDklEo" frameborder="0" allowfullscreen></iframe> Bónus: Rauðilækur
Q4U - Postpunk from the 80s, mostly in Icelandic. They’re still around. Here’s Sigurinn: <iframe width="420" height="315" src="http://www.youtube.com/embed/iiWcZKhWlQA" frameborder="0" allowfullscreen></iframe> Bónus: Snjóhvít
Samaris - Atmospheric minimal electro/triphop with clarinet. Very haunting. Here’s Góða Tungl: <iframe width="560" height="315" src="http://www.youtube.com/embed/_pKuzdMFE8k" frameborder="0" allowfullscreen></iframe> Bónus: Stofnar Falla
Nóra: Indie rock, ranging from upbeat and energetic to atmospheric and introspective. The more I listen, the more I like it. They sing entirely in Icelandic. Here’s Himinbrim: <iframe width="420" height="315" src="http://www.youtube.com/embed/w66kIAWBFs8" frameborder="0" allowfullscreen></iframe> Bónus: Sjónskekkja
Lockerbie - Post-rock, but with a bit more pop/rock than usually characterised by Icelandic post-rock. Here’s Snjóljón: <iframe width="420" height="315" src="http://www.youtube.com/embed/cUWzNsPHcEQ" frameborder="0" allowfullscreen></iframe>
Úlfur Úlfur - Hiphop with awesome backing percussion. They sing entirely in Icelandic. Here’s Út: <iframe width="560" height="315" src="http://www.youtube.com/embed/jCgbt73gD74" frameborder="0" allowfullscreen></iframe> Bónus: Ég er farinn
Pascal Pinon - D.I.Y., lo-fi, indie pop electronic. Many songs in Icelandic. Here’s Ekki Vanmeta: <iframe width="100%" height="166" scrolling="no" frameborder="no" src="https://w.soundcloud.com/player/?url=http%3A%2F%2Fapi.soundcloud.com%2Ftracks%2F71960187"></iframe> Bónus: Sandur
Sólstafir - Post-black metal, with elements of country and rock. They are amazing live. Their album Svartir Sandar is entirely in Icelandic and highly recommended. Here’s Fjara: <iframe width="420" height="315" src="http://www.youtube.com/embed/A6j7mUxGz20" frameborder="0" allowfullscreen></iframe> Bónus: Svartir Sandar
There’s lots of music that I’ve discovered that I didn’t cover here, but I only wanted to showcase the music I liked the most. Feel free to leave other suggestions in the comments.