Stokes 258 off 198 balls
Second fastest Test double century
Bairstow 150* - maiden Test century
Highest Test sixth-wicket stand (399)
Amla 64*, De Villiers 25*
England lead 1-0 in four-match series
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Image source, Getty ImagesJon Salinger: Why have England not bowled out South Africa yet?
Neil Burns: Stokes should have been given the new ball! He is blessed by the gods of cricket today!
Kristian Blade: Very impressive. But can they do it on a rainy Tuesday night in Stoke?
Broad back over the wicket to the right-handed Amla. Having had his captaincy roundly lambasted for the past day and a half, Amla is now faced with leading the Proteas fightback against a rampant England. Good luck, Hash.
Andrew Samson
BBC Test Match Special statistician
"Amla is averaging just 15 in his last seven Tests."
How can South Africa's day get any worse? Replying to a daunting 629, to lose one of your openers to a run-out in the third over is not far short of cricketing hara-kiri. Hashim Amla is the new man.
Geoffrey Boycott
Ex-England batsman on BBC Test Match Special
Image source, Getty Images"What did I say before the start? Their confidence is down, it's like a rolling stone, you can't stop it. Who would have forecast a run-out on a flat pitch like that. It's a gimme wicket for England."
Van Zyl run out (Compton) 4 (Eng 7-1)
South Africa fans, look away now. No, seriously, this is horrific. Van Zyl dtrops the ball to the left of point and starts jogging down the pitch. Dean Elgar starts to go then says no. Nick Compton scampers and collects the ball and Van Zyl is well short. Sorry, sorry viewing for the hosts.
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Two left-handers opening up for South Africa - and Broad has clearly planned this round-the-wicket approach. Van Zyl collects a single off the final delivery.
And it's Stuart Broad from the Wynberg End... Round the wicket to Van Zyl, who clips it off his pads for four. The chase is on.
Geoffrey Boycott
Ex-England batsman on BBC Test Match Special
"There has not been much movement in the pitch. They just have to bat well and at some stage they have to get the gremlins out of their minds."
A triumph! South Africans rejoice! The first over, bowled by James Anderson, is negotiated without alarm by opening pair Dean Elgar and Stiaan van Zyl. Two off the over. Trailing by 627. Sorry, couldn't help myself.
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So what can South Africa do? Can't say I envy them...
Image source, Getty ImagesStokes also hit more sixes in an innings than any England player in history, beating Wally Hammond's 11. Here's recap of both...
Stokes 258: 198 balls, 30 fours, 11 sixes.
Bairstow 150 not out: 191 balls, 18 fours, two sixes.
Geoffrey Boycott
Ex-England batsman on BBC Test Match Special
"It is a good pitch. South Africa have to get it into their head to not play bad shots, make them bowl you out. It is not about plundering boundaries; it is about assessing what to leave and getting a steady start. Get a platform and move on."
Some more figures for you, stats fans: in the course of that innings, Stokes' Test batting average has gone from 28 to 34, and Bairstow's from 28 to 33.
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Andrew Samson
BBC Test Match Special statistician
"The 550-600 took only 22 balls. They took 15.1 overs to get from 300-400 and just 11 overs from 400-500."
It's worth noting that Stokes and Bairstow added 399 for the sixth wicket - in only 58 overs - the highest sixth-wicket stand in Test history. Mightily impressive stuff.
Cook clearly wants to give his bowlers a blast at this bedgraggled South Africa side. Who can blame him? The hosts have been pummelled today - 312 runs in 39 riotous overs.