Laibach might just be the most absurd group ever to have existed. Their darkly comedic, high-camp cover versions of classic pop songs and mid-20th century totalitarian visual aesthetic is at once romantic, ridiculous and – since the end of the cold war – distinctly retro in tone. A decade ago, they seemed as irrelevant as a statue of Marshal Tito rusting in a scrapyard in their Slovenian homeland. With the release of new album Spectre, however, they openly comment on Snowden, WikiLeaks, protest movements, the wobbling Euro and the Arab spring. It's high time to start catching up with this most unusual and frequently misunderstood group.

Founded in 1980 in the mining town of Trbovlje (claim to fame: Europe's tallest chimney), Laibach hardly made things easy for themselves. Seeing TV footage of the Beatles and the Stones in their 60s finery, the young musicians realised that having some kind of uniform was a key element of the rock'n'roll myth. Then conscripts in the Yugoslav army, they used their fatigues as stage outfits, while smoke effects at early gigs came from stolen grenades. This, along with their black cross emblem and undefined critique of the political status quo, meant their aesthetic and intentions were open to interpretation, to the extent that some accused them of being Nazis. "We are fascists as much as Hitler was a painter," was their typically obscure response.

Laibach's cultural appropriation extends from the visual borrowing of totalitarian tat to their music itself. Behind the iron curtain they created their own playful musical culture out of the decontextualised scraps of what filtered over from the west. The songs of Queen are a recurring motif in their work, while one of their most popular covers is a trumpets-blaring take on 1985 hit Live Is Life by Austrian group Opus. In 2006, they recorded versions of 14 national anthems, including one for their art collective, NSK, which they had declared a virtual country in 1991, issuing their own passports. They've also borrowed from Churchill's speeches, the Beatles' Let It Be, the musical Jesus Christ Superstar and Bach.

This cheeky subterfuge came with a refusal on Laibach's part to explain themselves, which is what makes Spectre so fascinating, finding them commenting on current sociopolitical issues with characteristically bizarre flair. The subject matter is matched by their most accessible songs to date, with their harder-edged tendencies smoothed out in favour of Skrillex-at-cadets bangers such as No History. With a disdain for borders and an equal-opportunities critique of neoliberal capitalism and democracy, Laibach and the NSK can be seen as a precursor to supranational, leaderless organisations like Occupy and Anonymous. As they insist in song: "Resistance is futile".

Spectre is out in the UK on Mute on 3 Mar