We have had another great match involving Rafael Nadal and Serena Williams is through to the quarter-finals.
Roger Federer, Maria Sharapova, Novak Djokovic and Madison Keys are all in action tomorrow so join us then.
Bye for now!
Post update
Who's up next?
US Open 2016 finalist Karolina Pliskova. The eighth seed knocked out Australian Ashleigh Barty earlier today.
Getty ImagesCopyright: Getty Images
'I have grown up on this court'
Kanepi 0-6 6-4 3-6 Williams
Serena Williams: "It wasn't an easy match at all. She knows how to play and has a lot of big wins. She has had a great career.
"We always have tough matches so I am just happy to get through to be honest. She was hitting such big returns so I wanted to hit bigger second serves.
"I like it when players challenge me to do that. I think what I have improved most is my fitness. Coming back from having a baby is really hard!
"I can't wait because I want her to sleep in the bed with me every night. We are already best friends. I can't wait for Olympia be older and we can spend every day together!
"It was a really good match so I hope I can keep it up. I've literally grown up on this court. It is super, super special. Not many people can say that.
"I have been here since I was 15 and I'm still going!"
Post update
Kanepi 0-6 6-4 3-6 Williams
An 18-minute opening set whitewash, a little wobble in the middle and a commanding deciding third set sends Serena through.
No giant killing here today. Serena was just too good.
Game, set and match
Kanepi 0-6 6-4 3-6 Williams
A big serve. 15-0.
Then a forehand winner. 30-0.
Kanepi's backhand flies into the net. 40-0.
Then Serena manages to move her feet and swerve a forehand winner into the space behind Kanepi.
Game, set and match. Another win. Another quarter final. JOB DONE.
Post update
Kanepi 0-6 6-4 3-5 Williams*
Williams to serve for a place in the quarter-finals.
Post update
Chanda Rubin
American former world number six at Flushing Meadows
It all comes down to this - she has a chance to serve for the match.
Kanepi holds
*Kanepi 0-6 6-4 3-5 Williams
Kanepi kicks off with two aces then slams a forehand across court to change direction and go 40-0 up.
She then serves it straight into the body of Serena and the American sort of palms the ball away from her face - a bit like a five-year-old trying to hit a ball for the first time - and it flies over the baseline.
'Kanepi never lost her spirit'
Chanda Rubin
American former world number six at Flushing Meadows
After that first set it was difficult see even how Kanepi would get back into the match. Somehow she didn't lose her spirit.
But it's been a great turnaround and that has raised Serena's level.
Williams holds
Kanepi 0-6 6-4 2-5 Williams*
Kanepi sends Williams wide on the backhand but Serena somehow manages to keep it in. The Estonian returns it the same way and Williams dives onto it again. But at the third time of asking, Kanepi sinks it into the corner with her forehand.
Serena responds with an ace and Kanepi goes long on the next return.
Another big serve forces Kanepi's forehand into the net and Serena rounds it off with her 17th ace of the match.
Kanepi holds
*Kanepi 0-6 6-4 2-4 Williams
Double fault. 0-15.
An excellent rally follows. Some aggressive ground strokes from both players before Kanepi forces Williams long with a forehand deep into the baseline.
Another double fault. 30-30.
Williams goes long on the backhand. 40-30.
And Serena smashes into the net. Game Kanepi.
'Serena has raised her level'
Chanda Rubin
American former world number six at Flushing Meadows
Since the second set it's been an interesting contrast - that deep focus and inner fire is there with Serena again. She looks more confident. She's raised her level and that seems to have settled her down.
Williams holds
Kanepi 0-6 6-4 1-4 Williams*
Serena smashes a forehand winner and the crowd roars with delight.
Then an ace down the middle. 30-0.
And another ace. 40-0.
Kanepi goes long on the return. Game Williams.
Kanepi holds
*Kanepi 0-6 6-4 1-3 Williams
Serena does everything right to set up an open volley shot but she plays it too casually and Kanepi sprints into place before sinking it over the net and out of reach of the American.
And two errors from Serena quickly gives her 40-0 before Kanepi serves out the game.
That's 20 unforced errors from Serena now.
Post update
*Kanepi 0-6 6-4 0-3 Williams
I think my ears are still ringing from those screams from Serena.
Williams holds
Kanepi 0-6 6-4 0-3 Williams*
Serena's leaning back with every shot but Kanepi drags her backhand wide as the ball comes at her with too much power.
An ace gives Serena advantage (118 mph - her fastest serve of the match) and another big serve gives her the game.
Post update
Kanepi 0-6 6-4 0-2 Williams*
A lovely drop shot from Kanepi is out of reach from Serena and she ends up flat on the surface doing the splits.
Two fizzing serves bring her back to 30-15.
Then a double fault... 30-30.
And break point Kanepi.
EPACopyright: EPA
'Serena has rediscovered her calmness'
Chanda Rubin
American former world number six at Flushing Meadows
That's the demeanour we saw with Serena in the first set - she was calm and not rushed. She seems to have found that level again.
Williams breaks
*Kanepi 0-6 6-4 0-2 Williams
Game Williams. It was the opening she needed.
Post update
*Kanepi 0-6 6-4 0-1 Williams
Kanepi's backhand forces Serena off balance and she scuffs it into the net. She turns hastily, calls for the towels and gives herself a stern pep talk.
Her fury is unleashed in the next point. 15-30 to Serena.
Then a costly error from Kanepi hands Serena two break points.
Live Reporting
Saj Chowdhury and Emma Sanders
All times stated are UK
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Getty ImagesCopyright: Getty Images 
EPACopyright: EPA 
Latest PostPost update
That's all from us today.
We have had another great match involving Rafael Nadal and Serena Williams is through to the quarter-finals.
Roger Federer, Maria Sharapova, Novak Djokovic and Madison Keys are all in action tomorrow so join us then.
Bye for now!
Post update
Who's up next?
US Open 2016 finalist Karolina Pliskova. The eighth seed knocked out Australian Ashleigh Barty earlier today.
'I have grown up on this court'
Kanepi 0-6 6-4 3-6 Williams
Serena Williams: "It wasn't an easy match at all. She knows how to play and has a lot of big wins. She has had a great career.
"We always have tough matches so I am just happy to get through to be honest. She was hitting such big returns so I wanted to hit bigger second serves.
"I like it when players challenge me to do that. I think what I have improved most is my fitness. Coming back from having a baby is really hard!
"I can't wait because I want her to sleep in the bed with me every night. We are already best friends. I can't wait for Olympia be older and we can spend every day together!
"It was a really good match so I hope I can keep it up. I've literally grown up on this court. It is super, super special. Not many people can say that.
"I have been here since I was 15 and I'm still going!"
Post update
Kanepi 0-6 6-4 3-6 Williams
An 18-minute opening set whitewash, a little wobble in the middle and a commanding deciding third set sends Serena through.
No giant killing here today. Serena was just too good.
Game, set and match
Kanepi 0-6 6-4 3-6 Williams
A big serve. 15-0.
Then a forehand winner. 30-0.
Kanepi's backhand flies into the net. 40-0.
Then Serena manages to move her feet and swerve a forehand winner into the space behind Kanepi.
Game, set and match. Another win. Another quarter final. JOB DONE.
Post update
Kanepi 0-6 6-4 3-5 Williams*
Williams to serve for a place in the quarter-finals.
Post update
Chanda Rubin
American former world number six at Flushing Meadows
It all comes down to this - she has a chance to serve for the match.
Kanepi holds
*Kanepi 0-6 6-4 3-5 Williams
Kanepi kicks off with two aces then slams a forehand across court to change direction and go 40-0 up.
She then serves it straight into the body of Serena and the American sort of palms the ball away from her face - a bit like a five-year-old trying to hit a ball for the first time - and it flies over the baseline.
'Kanepi never lost her spirit'
Chanda Rubin
American former world number six at Flushing Meadows
After that first set it was difficult see even how Kanepi would get back into the match. Somehow she didn't lose her spirit.
But it's been a great turnaround and that has raised Serena's level.
Williams holds
Kanepi 0-6 6-4 2-5 Williams*
Kanepi sends Williams wide on the backhand but Serena somehow manages to keep it in. The Estonian returns it the same way and Williams dives onto it again. But at the third time of asking, Kanepi sinks it into the corner with her forehand.
Serena responds with an ace and Kanepi goes long on the next return.
Another big serve forces Kanepi's forehand into the net and Serena rounds it off with her 17th ace of the match.
Kanepi holds
*Kanepi 0-6 6-4 2-4 Williams
Double fault. 0-15.
An excellent rally follows. Some aggressive ground strokes from both players before Kanepi forces Williams long with a forehand deep into the baseline.
Another double fault. 30-30.
Williams goes long on the backhand. 40-30.
And Serena smashes into the net. Game Kanepi.
'Serena has raised her level'
Chanda Rubin
American former world number six at Flushing Meadows
Since the second set it's been an interesting contrast - that deep focus and inner fire is there with Serena again. She looks more confident. She's raised her level and that seems to have settled her down.
Williams holds
Kanepi 0-6 6-4 1-4 Williams*
Serena smashes a forehand winner and the crowd roars with delight.
Then an ace down the middle. 30-0.
And another ace. 40-0.
Kanepi goes long on the return. Game Williams.
Kanepi holds
*Kanepi 0-6 6-4 1-3 Williams
Serena does everything right to set up an open volley shot but she plays it too casually and Kanepi sprints into place before sinking it over the net and out of reach of the American.
And two errors from Serena quickly gives her 40-0 before Kanepi serves out the game.
That's 20 unforced errors from Serena now.
Post update
*Kanepi 0-6 6-4 0-3 Williams
I think my ears are still ringing from those screams from Serena.
Williams holds
Kanepi 0-6 6-4 0-3 Williams*
Serena's leaning back with every shot but Kanepi drags her backhand wide as the ball comes at her with too much power.
An ace gives Serena advantage (118 mph - her fastest serve of the match) and another big serve gives her the game.
Post update
Kanepi 0-6 6-4 0-2 Williams*
A lovely drop shot from Kanepi is out of reach from Serena and she ends up flat on the surface doing the splits.
Two fizzing serves bring her back to 30-15.
Then a double fault... 30-30.
And break point Kanepi.
'Serena has rediscovered her calmness'
Chanda Rubin
American former world number six at Flushing Meadows
That's the demeanour we saw with Serena in the first set - she was calm and not rushed. She seems to have found that level again.
Williams breaks
*Kanepi 0-6 6-4 0-2 Williams
Game Williams. It was the opening she needed.
Post update
*Kanepi 0-6 6-4 0-1 Williams
Kanepi's backhand forces Serena off balance and she scuffs it into the net. She turns hastily, calls for the towels and gives herself a stern pep talk.
Her fury is unleashed in the next point. 15-30 to Serena.
Then a costly error from Kanepi hands Serena two break points.