Kraftwerk closing a festival is a big deal. It’s an even bigger honour when the seminal German outfit reconfigure their set to acknowledge where they’re playing. Last Sunday, Kraftwerk performed the rarely heard “Airwaves”, from 1975’s Radioactivity album, within the honeycomb-windowed Harpa concert hall. They were paying tribute to Iceland Airwaves, the remarkable festival which was drawing to a close

While Lady Gaga’s conceptual antics left the crowd cold in Camden last Sunday, Björk’s Ally Pally spectacular last night showcased the musical artistry that sets her so far above other female pop pretenders. While Gaga’s affected oddities have always jarred with the mainstream sensibilities of her music, Björk’s strangeness perfectly fits and feeds her sound.

The last album released by Iceland’s múm was Early Birds, an archive trawl from 2012 which unearthed previously unheard material recorded between 1998 and 2000. Before that was 2009’s Sing Along to Songs You Don't Know. Smilewound is a comeback, and a welcome one. It’s also a statement of who múm are and closer in sound to an early album like Finally We Are No One than the – for them – relatively grandiose …Songs You Don't Know.

In the video made to accompany “One Half”, Julianna Barwick meets her inner goddess in a deserted multi-storey car park. When she closes her eyes, everything that is ordinary melts away and is replaced by a landscape that is as colourful as the previous scene is monochrome.

Characterising a country’s music by its most successful exports or what seem to be typical local styles is inevitable. With Iceland, the home of Björk and Sigur Rós, it’s easy to assume that ethereality, otherworldliness and plain oddness rule the roost. Of course, that’s not the case. The artists awarded the Kraumur prize for the best albums released in 2012 testify to Iceland’s broad musical palette. On the next page, our look at the Kraumur winners ranges from the hotly-tipped Ásgeir Trausti to, among other surprises, home-grown reggae.

Kveikur is really the first new album from Sigur Rós since 2008’s Með suð í eyrum við spilum endalaust. Their last, 2012’s Valtari, only had two fresh tracks and was otherwise redone offcuts or previously shelved material. The creative process leading to the appearance of Kveikur further differs from its predecessor as the band are now a three-piece, after the departure of keyboard player Kjartan Sveinsson.

Continuing its voyage through Scandinavia’s music, theartsdesk opens the latest chapter in Norway with Still Life With Eggplant, the 16th album from Trondheim’s prolific, long-lived, occasionally challenging and always vital Motorpsycho.

How John Grant would follow up 2010’s universally celebrated Queen of Denmark was a knotty dilemma. He could have settled into his role as the aberrant, self-lacerating, depression-fuelled, potty mouthed descendant of Lionel Ritchie and Eric Carmen. Instead, his new album takes him into new territories which again attests to his status as a singer/writer with no peers.

While Kafka specifically declined to indicate exactly what kind of creature Gregor Samsa becomes in his horrific overnight transformation, translators of the novella have gone for a variety of options: bug, beetle, cockroach or vermin. In this stage version, there is no attempt to imitate the appearance of any insect by means of costume or make-up; instead Gísli Örn Garðarsson uses his gymnastic skills to indicate movements alien to human beings while retaining Kafka’s underlying sense of a suffering man trapped in his new body.

When an artist calls the people of their hometown their family, it's usually a metaphor. In the case of Björk Guðmundsdóttir it’s actually true. Reykjavik has a population of only 200,000 and everyone is somehow related. But she's more than just the capital's favourite daughter: to the outside world the diminutive singer has become as emblematic of Iceland as its volcanoes and midnight sun. In turn, the uniqueness of the country helps fuel Björk’s individualism.