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Time, once more, for Reading + Leeds, the annual knees-up that has become a rite-of-passage for fans of rock, hip hop and grime, particularly teenagers freshly clutching their GCSE or A-level results.

Ahead of this year's festivlal we had a thought: who has been the greatest headliner in the festival's history? Radiohead, who opened with Creep in 2009? Patti Smith, for ushering in a punk takeover in 1978? That iconic 1992 performance from Nirvana?

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A dizzying sucker-punch of a show and a truly legendary set. The band members weren't on particularly great terms at the time, with frontman Kurt Cobain having become distant from the rest of the band due to a move to LA (drummer Dave Grohl and bassist Krist Novoselic had remained in Seattle) and a period of yo-yoing in and out of rehab. "We rehearsed once, the night before, and it wasn’t good," Grohl told magazine. Yet this performance was extraordinary from the moment Kurt was pushed onstage in a wheelchair to the last, venomous gasps of their rapid-fire seven-song encore. It was a lean, lithe show; a 90-minute flash of ferocious inspiration that would turn out to be Nirvana's last appearance in the UK. Kurt died in 1994.

People say the lads from Sheffield changed when they moved to LA, discovered hair products and recorded the classic rock-influenced AM, and those people are right. In 2014, a newly-bequiffed Turner introduced his band's new songs in a semi-slurred, quasi-American accent, with his only concession to the old times was a fond reference to their former hometown while at Reading ("We're the Arctic Monkeys from High Green, how you doing?) and a promise in Leeds that everyone would have "a reet laugh". And while they looked markedly more like rockstars, their set reflected their ascention to rock god level too. They were superb on both sites, proving - after an equally triumphant Glastonbury the year before - that they're one of the very few acts that formed in the noughties capable of headlining major festivals.

Reading's most imaginative headliner ever? The most inventive moment of Björk's incredibly inventive set was when she somehow made Isobel's joint jungle percussion and harpsichord sound entirely natural within a headline show of a major festival. That year, the Icelandic artist had released her third album, the alt-pop classic Post, and the set was loaded with its futuristic sounds. Asked in an on-site interview if she preferred large or small shows, she said: "To be honest, I like them little halls with about 500 people." Closing the night with It's Oh So Quiet, then, might have been her way of asking the enormous audience to chill out a bit.

This one was a charged and highly political set. When it comes to a headline show, there’s a lot to be said for making a memorable entrance - and Rage Against the Machine came onstage at Reading (but not Leeds) handcuffed, hooded and shuffling around in Guantanamo Bay-style orange jumpsuits. True to form, frontman Zach de la Rocha took the opportunity to talk (or rant) politics between songs, taking aim at Tony Blair and George Bush, while the sets on both sites were packed with hard-hitting tracks like Guerilla Radio, Wake Up and, of course, Killing in the Name. Rage had returned from a seven-year break and headlined the festival in the year of a US presidential election, as if to remind everyone what a powerful political voice they were.

It's, well, crept back into their sets recently, but Radiohead are well-known for not being very keen on their massive crossover hit Creep. In fact, they're about as likely to play the song as Thom Yorke is to voice the smiley face in The Emoji Movie 2. It was something of a shock, then, when the band began their 2009 Reading (but not Leeds) set with that lilting, familiar guitar melody and, "When you were here before..." Even more unexpectedly, Thom had greeted the crowd with a firm, "Wassup!" After, familiar material (Karma Police) sat comfortably with more obscure work like 15 Step, which they opened with in Leeds.

Back in 2001, some considered it outrageous that Eminem was allowed to take his confrontational lyrics on tour in the UK and there was a picket line at his Manchester Evening News Arena show ahead of headlining Reading + Leeds. It was the show your mother warned you about, as well as a zeitgeist-defining moment.

Anarchy might have been in the UK the year previously, with the Sex Pistols' Never Mind the Bollocks having rattled the nation, but it was Patti Smith's 1978 appearance that saw Reading go all anti-establishment. The bill was studded with punk bands such as Sham 69 and Penetration, but it was the New Yorker's headline set that truly put the boot into the festival's reputation for classic rock. She played the likes of Gloria and Because the Night, and also cleverly covered The Who's My Generation and The Byrds' So You Want to Be a Rock 'n' Roll Star.

Reading 1983 saw a stylish, fond farewell from one of rocks most enduring groups. This wasn’t quite the last ever Thin Lizzy concert - that happened a week later in Nuremberg, Germany - but it was the Irish band's final show in the UK. Frontman Phil Lynott seemed to be having the time of his life, just three years before his death, hamming up the introduction to The Cowboy Song by imploring the audience to give a "coyote call". The group had already forged a relationship with the festival, having headlined it in their heyday in 1977, so this was something of an emotional send-off for Lynott and the boys, who wouldn’t be back in town any time soon.

How on Earth do two people sound as massive as The White Stripes sounded as they destroyed Reading and Leeds' Main Stages with Seven Nation Army in 2004? There's some black magic at work, no doubt, and the headrush that is Fell in Love with a Girl was equally epochal. At Reading, one of the most dynamic moments saw Jack White play a quiet keyboard part in the midst of I'm Finding It Harder to Be a Gentleman before returning to the business of playing guitar like he was trying to saw it in half. The Leeds crowd was treated to a cover of Bob Dylan's Love Sick.

Instead of relying on heritage acts as headliners, Reading took a punt on the talent of today when Foals co-headlined with dance duo Disclosure in 2016. It was thrilling to see Yannis Philippakis and co. graduate to the Main Stage, having started their ascent up the Reading + Leeds bill almost a decade earlier. The performances on both sites were incendiary, boasting flamethrowers, a stage dive from Yannis and a blistering three-song encore of What Went Down, Cassius and Two Steps, Twice.

2018 saw Compton rap king Kendrick Lamar at the top of his game. A year prior, he concluded his trilogy of modern classic albums - Good Kid, M.A.A.D City (2012), To Pimp a Butterfly (2015), Damn (2017) - and had just became the first non-classical musician to win a Pulitzer Prize. Reading + Leeds was something of a victory lap from King Kendrick, then. With his unrivalled flow, effortless cool and formidable stage presence, Kung-Fu Kenny's set had everything. Show-stopping visuals? Check. Raw talent? Yep. Hit after hit? Of course. Lamar proved just why he’s loved by critics and fans alike. Long live the King.

• Reading + Leeds 2019 runs from 23-25 August. Watch on 大象传媒 iPlayer. Listen on 大象传媒 Sounds.