The National's stunning Eden Sessions gig shows why they're one of the world's greatest bands

When I told friends and family I was going to see The National I invariably got a "who?". Therein lies the weird dichotomy - they're the world's biggest band people haven't heard of.

No big hits, just a steady of stream of inventive albums of personal existential crises and faltering romance; the American Smiths, if you like, without sounding anything like Morrissey and Marr. Through early word of mouth and festival touring they've become huge by stealth.

So it was a genuine thrill when The National were announced for the Eden Sessions, and they didn't disappoint with an epic 26-song set, which differed quite a bit from their Glastonbury headline slot two nights before.

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No fancy set production because they don't need it - they let the songs do the talking thanks to the consummate musical skills of the two sets of brothers. Twins Aaron and Bryce Dessner are the loveliest, geekiest, most unlikely 'rock stars' out there. Aaron, who's now got an alternative career as a Taylor Swift collaborator, is a bit of a guitar god on the sly (or is it Bryce?), while the rhythm section of Scott and Bryan Devendorf provide sturdy support.

Throw in touring members on keyboards and trumpet and the band is hard to beat live. The not-so-secret weapon, of course, is frontman Matt Berninger. He may look like he's just absentmindedly walked on stage after taking a nearby sociology lecture, but like Jarvis Cocker he has a nervy theatricality which is utterly mesmerising. If he started a cult, you'd follow Matt all the way to Waco.

Fans of the band got a bit of a dream set - songs from nine of their ten albums, the shout-alongs as well as adored deeper dives. Eucalyptus provided the first crowd participation thanks to its incessant chorus of "You should take it, cos I'm not gonna take it" - very National that, a song about a splintered couple deciding who should get what when they move on.

They can do beauty (I Need My Girl, a glorious Light Years) and they can do raw (Graceless, the second half of Space Invader). They can do the big singalongs (Bloodbuzz Ohio, Terrible Love and Fake Empire - arguably their three best known songs) and they can do strange (Smoke Detector which doesn't really get anywhere but reaches nowhere perfectly).

From cuddling a woman in the front row, who held up a sign saying "This is my 30th show, can I get a hug?", to bringing out a birthday cake for drummer Bryan and then threatening to throw it into the crowd which he sort of did in the end, Berninger was a delight; one minute excruciating midlife angst, the next laughing at himself for posing on a spotlight and then falling off it.

The cable guy needs a special mention too. The singer has a habit of going for long walks through the crowd, disappearing completely during the mighty Mr November. Cable guy always reels him back in.

The wonderful This Is The Kit supported - their jazzy, jittery folk pop, where Wire meets Pentangle, was perfect for a summer's evening. A special moment came during The National's set when This Is The Kit's Kate Stables joined the band for stunning versions of I Am Easy To Find and Rylan (definitely not about that Essex bloke).

The National provided a beautiful end - bittersweet 20-year-old ballad About Today exploded into unexpected noise, which was as thrilling as when The Wizard of Oz goes from mono to technicolour, while the crowd hollered back every word of the final, acoustic Vanderlyle Crybaby Geeks, showing their love for a very special band.

From the sublime to the Rick Astley tonight - the utter joy of the Eden Sessions, there's something for everyone.