Kings of Leon, Hyde Park, London

Just how have Kings of Leon got so big? For ages they were no more than a middleweight indie band with a little bit of underground cachet and a smattering of profile. Suddenly, they're everywhere, headlining festivals, rocking daytime radio playlists, and soundtracking Saturday afternoons in Argos.

It was last year that they really hit the huge-time, but even with their 18 hard-earned months of near-ubiquity, it's hard to process the sheer extent of the crowd here in Hyde Park. Apparently, there are 65,000 people here tonight – a figure beyond the wildest dreams of all but the most enormous bands.

Singer Caleb Followill at times seems somewhat shell-shocked. As well he may: there are tens of thousands of people plastered with beatific smiles joining him on every chorus. He thanks the crowd constantly, always with a note of bewilderment, as though his band's popularity is a mystery even to him.

However astonished they are to be playing such a colossal concert, it doesn't show in their playing. They're impeccably tight, and they know each other well enough to allow themselves a few musical indulgences. They've been careful enough to put extra mass into the songs, and they'd easily fill the park even without 130,000 lungs belting their words back at them.

Musically, they're absolutely spot-on. They play it like they're at one of those classic rock shows of times past – soaring, Seventies-style riffs powering out of the PA in gloriously sunny conditions. They don't really throw the shapes that the occasion deserves, and they don't rock out with full abandon, but they're nearly there.

The encore is wholeheartedly blissful, played as the sun sets and twilight creeps in across a purpling, cloudless sky. Darkness falls to the strains of megahit "Use Somebody"; we're all still dancing after more than two hours, and it's abundantly clear why this band is so big.