40. Blow Out (1993)

Save a riotous airing on 1994’s Live at the Astoria, Pablo Honey’s closer rarely intrudes on Radiohead lore. A shame – because it’s a tantalising finale: the sound of a nervous band storming the city limits and glimpsing Valhalla.

39. The Daily Mail (2011)

Culling this weirdo jamboree from the tranquil King of Limbs was a no-brainer. As a stand-alone, though, it’s irresistible, suggesting an unlikely kinship between Radiohead and the venerable pop cynic Randy Newman: musical-theatre flair weaponised against tabloid hysteria.

38. Spectre (2015)

The band’s rejected Bond theme has assumed the identity of a curiously viable Radiohead song. Thom Yorke is persuasive – if not exactly suave – in character as the secret agent, but credit Jonny Greenwood, as we often must, with its emotive thwack.

37. Kid A (2000)

Driven to despair by OK Computer’s runaway success, Yorke faced a perilous choice: sacrifice his sanity in exchange for astronomical fame or persuade Ed O’Brien to get into Autechre. On Kid A, the second option won out: sequestered away with Greenwood, Yorke produced much that haunts and a little – like the title track – that gleams.

Yorke performing in Manchester in 2012. Photograph: WENN Rights Ltd/Alamy

36. Packt Like Sardines in a Crushd Tin Box (2001)

After decrying consumerism, swerving into outre avant-rock and selling millions of records anyway, Radiohead learned the hard way that condemning society would just make them even richer. Trying a new tack, the Amnesiac opener layers anxious ticks and gamelan-style chimes before gently lampooning a “reasonable man” with an uneasy conscience.

35. Burn the Witch (2016)

Once the band’s secret weapon, Greenwood is now a garlanded composer and Radiohead’s melodic powerhouse. Finally entrusted to build an arrangement from scratch, he turned the live favourite Burn the Witch into this orchestral jaunt. The iffy tour version – shorn of strings and charm – attests to his handiwork on the recording.

34. Creep (1993)

Radiohead’s biggest hit is so beautiful and corny, it is impossible to accept it on its own terms. “I want you to notice when I’m not around,” Yorke broods, a perfect lyric he probably hates. In the end, the band’s disavowal of the song sent its credibility full circle. Nowadays, Creep is a joke, but we’re all blissfully in on it.

33. Scatterbrain (2003)

An unsung gem from Hail to the Thief, Scatterbrain prescribes halting rhythms and deconstructed chords to a narrator fretting over his identity. As birds and newspaper pages thrash in a gale, Yorke, too, longs for chaos. The tantalising, unresolved chords mock him, but enchant us.

Radiohead … 2016 vintage. Photograph: PR Company Handout

32. Just (1995)

Post-Creep, Radiohead were poised between grunge and Britpop. Just is a time capsule at the crossroads: hailstorm distortion meets perky hooks, wily vocals and – Yorke’s mischievous challenge to Greenwood – an absurd pageant of guitar chords. The chorus flips the grunge ethos on its head, swapping self-loathing for theatrical vitriol.

31. 2+2=5 (Live at Earls Court) (2004)

As the Iraq war protests floundered, Yorke sporadically logged on to radiohead.com to denounce New Labour and the warmongering “thief” in the White House. 2+2=5 is his polemical anthem for the era of mass-broadcast deception and enhanced interrogation techniques, captured thrillingly in this Com Lag EP version.

30. Morning Bell (2000)

Kid A’s unorthodox breakup song was later resurrected as Morning Bell/Amnesia (“like a recurring dream,” Yorke observed), but keep room in your heart for the cold-sweats original. Only a melody so blissfully innocent could withstand such jittery, nightmarish contortions.

29. No Surprises (1997)

No Surprises.

Radiohead’s most misunderstood protagonist has it made: the house, the garden, the heart full up “like a landfill”, the “job that slowly kills you”… and how lovely it all sounds. Can a radical conscience coexist with suburban comforts, No Surprises asks? For all that it soothes, this one is pessimistic.

28. Lucky (1995)

The Bends had vamped and snarled for the gallery, but Lucky – recorded for a War Child compilation – signalled deeper concerns and higher stakes. Creeping riffs, melodic blasts and shameless melodrama laid the groundwork for OK Computer while cementing the band’s partnership with the producer Nigel Godrich.

27. There There (2003)

After the divisive Kid A/Amnesiac era, Hail to the Thief’s lead single felt diplomatic – no more sacrilegious than Blur’s experiments at around the same time. Its hooks and arrangement were deceptively crafty, though, making its turbulent climax hard to shake.

26. Where I End and You Begin (2003)

Sequenced in the mid-album swamp of Hail to the Thief, Where I End and You Begin is a maligned masterclass in broody synthpop. With Yorke “up in the clouds” and Greenwood making spaceship sounds, the rhythm section straps in and goes full New Order, hurtling towards an ecstatic climax.

25. Everything in Its Right Place (2000)

Where OK Computer declared “I am born again”, Kid A dives straight into obfuscation: its opener’s choppy vocal gibberish more closely resembles the “unborn chicken voices” plaguing the Paranoid Android. Like David Byrne before him, Yorke had renounced his authorship to flirt with self-erasure, yielding to gorgeously sunlit synths.

24. Harry Patch (In Memory Of) (2009)

A later-career treasure, Radiohead’s tribute to the last surviving combat soldier of the first world war shows how much ground they have barely touched. With just a funereal, cinematic string section for company, Yorke sends his falsetto out over the trenches, an innocent witness to “demons coming up from the ground”.

23. Daydreaming (2016)

Beneath the tiptoeing pianos, Daydreaming is a gut-wrencher. In a lyric some have linked to his late long-term partner, Yorke finds himself sleepwalking “beyond the point of no return”, before repeating a mournful mantra, “Half of my life”, played in reverse. The timeline matches that relationship’s duration and, equally, the lifespan of Radiohead.

22. Subterranean Homesick Alien (1997)

Plunged into a shimmering dreamscape, Yorke observes a fleet of aliens surveying humanity. What, the interlopers wonder, is up with these oddballs? In fact, it’s all an excuse for Yorke’s alienated narrator to ask himself: am I the problem or is society? Radiohead exist to petition for the second option; here, however, was sweet ambiguity.

The band circa 1996. Photograph: Trinity Mirror/Alamy

21. A Wolf at the Door (2003)

Insufficiently radical to some, Hail to the Thief staged a hit-and-miss venture into a new songwriting idiom. Among the hits, far and away the zaniest track was the album closer: a nightmarish waltz resembling a mutant Bends castoff, capped by a curmudgeonly rap about capitalist thugs and politicians taking cream pies to the face.

20. Like Spinning Plates (2000)

After hearing their song I Will being rewound on tape, Yorke decided the backwards version was “miles better” and recast it as Like Spinning Plates. A complementary piano version, from the I Might Be Wrong live album, brings its spectral beauty into focus. Once you’ve heard it, the original becomes indispensable.

19. Motion Picture Soundtrack (2000)

On an album bound to futuristic threats and technologies, Motion Picture Soundtrack’s melancholy harmonium, fluttering harps and rolling, beatless expanse suggest a return to uncorrupted Eden. Tellingly, it originates from the band’s youthful origins as On a Friday.

18. Weird Fishes/Arpeggi (2007)

Nigel Godrich settles into cruise control on this In Rainbows highlight, a rare haven from the band’s omnipresent dread. Instead, Weird Fishes/Arpeggi evokes an all-too-perfect harmony: cascading arpeggios enchant while fragmentary lyrics caution against the lure of false prophets.

17. True Love Waits (2016)

Even when they’re not facing the abyss, Radiohead songs tend to operate in its general vicinity, albeit without revealing what led there. But True Love Waits – sketched on an earlier live album and perfected 15 years later – conceals nothing: the abyss, listener, is love. “I’d drown my beliefs to have your babies,” Yorke confesses woefully, wonderfully.

16. Airbag (1997)

After The Bends, the smart money had Radiohead scaling up for festival supremacy. OK Computer’s opener took the bait then veered left: first the brain-melting deluge, then ripples of funk, a sexy drum lurch and some Maxinquaye basslines. Yorke – summoned “back to save the universe” – presides over the melee like a despairing god.

15. Videotape (2007)

On In Rainbows, Radiohead’s cosiest album, Videotape is refreshingly, passionately despondent. Yorke vaguely evokes horrors – surveillance-state ennui, digital isolation, the gaze of an unforgiving deity – in a death-row drawl. Then, a change of heart: perhaps it was “the most perfect day I’ve ever seen”, after all.

14. Polyethylene (Pt 1 & 2) (1997)

Radiohead’s greatest (although, somehow, not first) antiplastic jeremiad, this Paranoid Android B-side thrashes and struts like The Bends’ glam evil twin. Far from the ham-fisted Fake Plastic Trees, Polyethylene is all malevolent snarl, bouncing off the walls in defiance of middle-class ecological hubris.

Thom Yorke in 2013. Photograph: Phil Fisk/The Observer

13. Knives Out (2001)

The impenetrable Amnesiac debunked industry rumours that Radiohead were primed for a bankable comeback – but amid that album lay this meat-and-potatoes rocker, its scurrying riffs, mystic ambience and cannibalistic lyrics qualifying as glorious light relief.

12. Street Spirit (Fade Out) (1995)

Yorke once compared it to “staring the fucking devil right in the eyes” and knowing “he’ll get the last laugh”. Street Spirit makes for a spectacular showdown – a grand, doomed surrender. If you need a chaser, consider another vintage Yorke quote: “If I was happy, I’d be in a fucking car advert.”

11. Sail to the Moon (2003)

Yorke’s lullaby for his infant son has a distinctly bad-dreams vibe about it. Someone should probably have a word. Still, his good intent shines. “Maybe you’ll be president,” Yorke rasps over writhing guitars. “Or in the flood, you’ll build an ark and sail us to the moon.” For young Noah, big sustainable footwear to fill.

Early 90s. Photograph: Getty Images

10. My Iron Lung (1994)

A dig at Creep’s annoying popularity, My Iron Lung uses catchy hooks and brawny riffs to rally against commercialisation. It risks sounding bratty – it is bratty – but from insolence they fashioned a new identity: stadium-rock agitators declaring war on hypocrisy and greed – particularly their own.

9. Exit Music (For a Film) (1997)

Bewildering, still, that Radiohead composed this monstrous ballad for Baz Luhrmann’s 1996 flick Romeo + Juliet, partly because it’s a high-stakes blockbuster of its own. Yorke has never sounded gloomier, with poisonous murmurs rising to a bloodcurdling fever pitch.

8. The National Anthem (2000)

At first conjuring arthouse delirium – improv skronk, transistor radio babble, warbling ondes martenot – Kid A’s jazz-rock monster morphs into an electrical storm of brilliantly layered tension. Like a Mingus requiem, The National Anthem’s power lies in the staggering weight of what is unresolved.

7. Nude (2007)

In Rainbows’ online release prompted a global listening event anticipated unlike any since. Three tracks in, the magic happened. After kicking around in Radiohead lore for more than a decade, Nude had found stunning form, first by channelling Björk – choppy coos, weeping strings – and then in a finale as bright and penetrating as dawn.

6. Idioteque (2000)

Yorke says he poured his most stubborn anxieties into Idioteque, which may explain why this pumping club tune – a formal anomaly – feels like Radiohead’s chaotically distilled superego. Ecological dread, big-tech menace and catastrophic panic prevail, but that shiver-inducing synth sample doles out propaganda for hope.

5. Karma Police (1997)

Karma Police.

Part literary dystopia, part John Lennon in a Pixies T-shirt, Karma Police is an enduringly odd superhit: at once relatable, inscrutable and chilling. Such nuance is now Radiohead’s bread and butter, but only so because Yorke learned, after much saccharine bumbling, to consolidate his bleak and mawkish impulses into one.

4. Pyramid Song (2001)

Since Kid A skimped on promo, Pyramid Song technically followed up the hit single No Surprises. For casual fans, a few surprises: lyrics alluding to Hermann Hesse’s Siddhartha, piano seemingly exhumed from ancient civilisation and a newly spiritual Yorke, swimming with “black-eyed angels” and a shoal of exes towards some nebulous afterlife. Torture for some; otherwise, cult-making.

3. Reckoner (2007)

Rock orthodoxy holds that a great band’s nerve centre resides in a single genius – two at a push. Radiohead’s greatest ensemble piece kills the myth for good. At first innocuous, Reckoner unspools a full house of virtuoso performances engulfed by Godrich’s winter-blanket production. It soothes then soars.

2. How to Disappear Completely (2000)

Few admit it, but Radiohead’s home turf is the desperately uncool milieu of avant garde balladry. How to Disappear Completely, a masterpiece of the form, orchestrates a stage-fright reverie with fragments of Robert Wyatt and Penderecki. In Kid A’s supposedly cold heart it is pure affirmation: melancholy and light.

1. Paranoid Android (1997)

The video for Paranoid Android.

As Britpop plunged from grace, Radiohead planted a revolutionary flag in the mountaintop. With OK Computer’s salvo, they shed the skin of insurgent oddballs, ditched grungy radio rock and electrified the popular imagination. Paranoid Android draws less from contemporaries than their ancestors, notably – audaciously – within prog. The seven-minute odyssey plunders rock’s then-forbidden city with burbling basslines and guitar wizardry so breathtaking nobody bothered to revoke Greenwood’s daytime-radio visa. Elevated by Yorke’s apocalyptic babbling and heavenly falsetto, we witness operatic scale and drama (“The dust and the screaming! The yuppies networking!”) in a ludicrously catchy anthem. Paranoid Android stormed the castle and raised the drawbridge on rock’s imperial era.