Postpublished at 02:39 British Summer Time 6 September 2017
Jeff Tarango
Former professional tennis player on 5 live sports extra at Flushing Meadows
An incredible day of tennis already just keeps getting better.
Williams beats Kvitova 6-3 3-6 7-6 (7-2) to reach semi-finals
Roof closed during second set on Arthur Ashe Stadium
Stephens beats Sevastova 6-3 3-6 7-6 (7-4) to make last four
Carreno Busta beats Schwartzman 6-4 6-4 6-2 to make men's semis
Alex Bysouth and Mike Henson
Jeff Tarango
Former professional tennis player on 5 live sports extra at Flushing Meadows
An incredible day of tennis already just keeps getting better.
*Williams 6-3 3-6 5-5 Kvitova
Kvitova holds. Superb stuff from both players. A powerful service display from the Czech.
Williams 6-3 3-6 5-4 Kvitova*
Williams is just guiding the ball back into Kvitova's half of the court now, waiting for the Czech to make a mistake.
So what does she do? Softens the hands, adjusts the grip and guides the cutest of drop shots just over the net to go 40-0 up.
Gigi Salmon
BBC Radio 5 live sports extra commentator at Flushing Meadows
All previous meetings between these two have gone the distance. This one is no different.
Williams 6-3 3-6 5-4 *Kvitova
Petra Kvitova is serving to stay in the match, to stay in the tournament.
The first is big, punchy and Williams won't return that. The second the American sends long.
Williams 6-3 3-6 5-4 Kvitova*
Williams holds. The most punishing game of the match so far, but it's the American who comes out on top.
And breathe.
*Williams 6-3 3-6 4-4 Kvitova
The brilliant to the bizarre. Williams has Kvitova scuttling from one side of Arthur Ashe to the other, but faced with a simple volley to close the game out, she gets more frame than a Mother's Day morning and finds the net.
Jeff Tarango
Former professional tennis player on 5 live sports extra at Flushing Meadows
Both players sucking wind a little bit, like a sprinter after a 200m.
*Williams 6-3 3-6 4-4 Kvitova
There it is, the ace she so needed. Williams shrugs off any pressure she might be feeling with a 115mph serve that leaves Kvitova rooted to the ground.
And she follows up with... a double fault. Friends star Jennifer Aniston doesn't look impressed.
*Williams 6-3 3-6 4-4 Kvitova
Kvitova isn't about to give this up without a fight, she has Williams sprawling to her right but the American can't make it. Williams is on the run again a point later as a searing Kvitova return fizzes beyond her.
It's deuce.
*Williams 6-3 3-6 4-4 Kvitova
Venus Williams takes a few deep breaths, she needs them after Petra Kvitova had her running across court - a challenge on either side, but it's Williams' point.
The American then steps up and slams a huge forehand past Kvitova to go 40-0 up.
Gigi Salmon
BBC Radio 5 live sports extra commentator at Flushing Meadows
Three aces, one clipped the frame - a perfect game for Petra Kvitova.
*Williams 6-3 3-6 4-4 Kvitova
Right then, it's make or break. Kvitova reaches for a new racquet, and slings a stormer of a serve past Venus, who doesn't even blink.
Ice cold, as a composed as anything, she fires down four unreturnable serves to hold. Wow.
Jeff Tarango
Former professional tennis player on 5 live sports extra at Flushing Meadows
This crowd is on its feet, cheering for Venus.
Williams 6-3 3-6 4-3 *Kvitova
Kvitova looks weary. She stares at a backhand that sails long and Williams storms into a 40-0 lead.
It's Williams back in front.
Jeff Tarango
Former professional tennis player on 5 live sports extra at Flushing Meadows
Weren't we here a few hours ago with the other women's quarter-final (Stephens-Sevastova) with the exact same scoreline - 6-3 3-6 3-3?
*Williams 6-3 3-6 3-3 Kvitova
Brilliant from Venus. She's standing up to Kvitova's every move now and earns herself a break point.
It was a swinging backhand return that did the damage. And a double fault follows.. out of nothing, Williams breaks.
Williams 6-3 3-6 2-3 *Kvitova
Cracking rally from these pair of former Grand Slam champions. Cross-court, high speed, inch-perfect, until Williams' effort goes awry.
Kvitova moves into a 30-0 lead, but can't scramble beyond her baseline quick enough to add to that advantage.
Jeff Tarango
Former professional tennis player on 5 live sports extra at Flushing Meadows
This crowd is really trying to get behind Venus and get her that energy, get her that comeback. But from what I've seen from Kvitova in the first five games of this set, she can win this tournament.
Williams 6-3 3-6 2-3 *Kvitova
As Venus Williams' effort increases, so do the decibels in which she screams her way into every point.
She successfully navigates a couple of Kvitova bombardments to hold.