British space-rockers Muse have always been intergalactic.

They tend towards the epic. Their latest tour is no exception. Currently playing in arenas in the US (as opposed to their usual stadiums elsewhere in the world), they are in the ascendant here, expanding beyond the confines of the space into undiscovered dimensions. The show is like a million brilliantly-lit synapses firing simultaneously, Pink Floyd on acid, fast-forwarded into a monumental version of 2001:A Space Odyssey (their stage set has monoliths and is full of stars, and spending two hours watching it is like traveling through the star gate, over and over again), digitally spliced into an enhanced, particularly psychedelic version of the original Star Trek series, remixed into the atmospherically heavy, majestic and futuristic landscapes of Blade Runner, and with all the paranoia of the best sci-fi, and all the beauty – as Exogenesis: Symphony Part I plays out, digital imagery overloads our sensory capabilities to behold it as we see starry visions, endless space, poetic IMAX-level visuals like the more out-there scenes from Avatar, only more so.

And that’s just one song.

They play many more over the two hour show, and, having learned well from their stint supporting U2 on their 360 stadium tour last year, Muse work the stage, in the round, allowing fans on all sides to watch Matt Bellamy coax howls and whispers, screams and tears, roars and huge, monster crunching from his guitar as he croons and soars, playing furiously, with molten metal fluidity. The band is extraordinarily locked together, and they lay down crushing grooves as though several Led Zeppelins were on stage with a few Metallicas and Slayers; only Muse make it look effortless. They blend metal, indie-rock, orchestral majesty, virtuoso piano like Chopin. Imagine a supergroup comprised of Joe Satriani, James Hetfield, Thom Yorke, Jeff Buckley, a bevy of conspiracy theorists, an alien and Debussy, and you might get close to understanding the truly unearthly being that is singer-guitarist Matt Bellamy. The other two are peerless: Dominic Howard sounds like an army of drummers and delivers a brutal, monumental barrage of monstrous, relentless proportions, while Chris Wolstenholme transforms his bass from the super-charged engine of the Muse spaceship  into a fifties B-movie monster prowling menacing and vast through the future cityscapes created by Matt and Dominic, thrashing around, pounding at impossible speeds, rising up to loom over the whole.

The Muse experience is an insane, mind-dazzling rush delivered with absolute control, precision and power. They are becoming themselves in the US at last: powered by the triple engine of the Twilight soundtrack connection, the U2 support gig last year, and the release of what might be their best album yet in The Resistance, a slinky, hard-rocking, melancholy and space-operatic masterpiece with no inhibitions: the most perfect blend yet of the old-fashioned romance, paranoia, beauty and gazing into the far reaches of the universe that typifies Muse.