Hvarf-Heim, released at the same time as the Iceland tour film Heima, is split into two halves. Disc 1 contains three new songs and two new recordings of old songs, while disc 2 contains acoustic recordings, giving a different kind of companion soundtrack to Heima.
First section (or disc 1) is called Hvarf, which means "disappeared" in Icelandic, and it seems like the band have to withdraw from the society and live in obscurity. Opening track "Salka" is a medium-slow number, with a guitar intro that signal the beginning of another out-of-this-world journey with Sigur Ros. Musically, it sounds like a song from the Takk... period, Jónsi's high pitch voice still cleanses the listener's ears, and the ending brings us from the climax to the silence. First single "Hliómalind" acts as a buffer, just like "Hoppípolla" after "Glósóli" on Takk..., from a wall of sound to a melodic track.Of course, "Hliómalind" is more attached to the European rock band style than "Hoppípolla". The third track "Í Gær" takes on the route to their early composition. Starts off with a calm and quiet intro by a music box, it suddenly bursts into a giant guitar wall of sound. This song is more musically dramatic compared to the previous two tracks, with its ups and downs in between. Followings are "Von" and "Hafsól", both are taken from their debut album Von. "Von" is transcended from its low-key keyboard backbone, to become ambient-like stings and guitar. While the original version gives people the thought of finding hope in the dark, the new version offers less sadness and brighter hope to the future. "Hafsól" is a new mix from the version appeared on the single "Hoppípolla". With more added percussion parts, the song is more tighter and excited towards the end.
Second section (or disc 2) is called Heim, which means "home" in Icelandic, and it features acoustic songs recorded from different location during their Iceland island tour. When it was announced that Sigur Ros would record the second half in acoustic, general response is to long for how they are going to take down the songs. Surprisingly, the versions appeared on Heim has a more positive feeling than the originals. With most electronic instruments stripped off, it takes away part of the isolation in Sigur Ros music, and becomes more personal with the listener. Taken from , (a.k.a. ) exchanges electric guitar with organ, brings the curtain up for the this second act. 、 (a.k.a. from ) and are kept with their basic structure when re-arranged for the acoustic setting. Among these, caught the attention as it captures the band's affection and unity, giving the song a freshness and beautiful sounding. Ending this half and the album is the song that appears both in this and the first half. continues the search for hope from the previous half. Here, it feels like the band are on a boat under sunset, sailing ahead to their unknown future.