Right, this live text, like Madison Keys, is heading out home after a creditable performance.
Just a reminder that the schedule is out for tomorrow.
Andy Murray v Kevin Anderson at approximate 19:30 BST and Jo Konta has got a prime-time slot, taking on BBC Sport columnist and two-time Wimbledon champion Petra Kvitova in the first match of the night session.
That gets going at midnight tomorrow.
Bye for now.
Post update
GettyCopyright: Getty
The match stats actually tell quite an interesting story.
Madison Keys hit more winners, 24 to Serena's 18, but really suffered on second serve, losing 18 of her 28 points off that shot.
Post update
Getty ImagesCopyright: Getty Images
Serena Williams, speaking on court: "It was really important to get a good start. Madison is so powerful and knows how to win big matches. My only chance was to start fast.
"I stayed in there and did the best I could. I relaxed, got a few lucky shots and got the break.
"My serve was much better today. I had to, because Madison has a great serve.
"I don't feel any pressure. Winning four in a row at Wimbledon was amazing. Now I have a chance here to make it five and the New York crowd is pushing me on. It makes me want to to perform and do better.
"The only difference to playing Venus now is that we're a lot older. She's playing great. I have to really be ready for her. At least one of us will be in the semis."
Post update
Serena Williams tells the on-court interviewer that she doesn't feel any pressure over the calendar Grand Slam, having bagged the Serena Slam (holding all four Grand Slam title, but not having actually won them all in the same year) at Wimbledon.
Full quotes on the way as Serena blasts a trio of signed balls to the cheap seats.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"What an impressive match from Serena. She served really well."
Game, set and match
Serena 6-3 6-3 Keys
Serena Williams, Lady Luck and service gremlins are all conspiring against Madison Keys as she folds out of the match as a fluky net cord goes against her and she then double-fault on the world number one's first match point.
Cue a curtsying and pirouetting Serena in the centre of Arthur Ashe.
Post update
Post update
Serena 6-3 5-3 Keys
Serena Williams is still crushing the ball and, if anything, is accelerating for home.
She brings up 40-0 in a twinkle and, although Madison Keys lobs a screwdriver in her gears momentarily with a superb forehand winner, Williams closes out with an ace on the next point.
Williams breaks
*Serena 6-3 4-3 Keys
After purring for most of the match, Madison Keys' game suddenly comes apart like a clown car.
The American duffs long with a squeal of dismay to hand Serena Williams a break point at deuce and, at the sixth time of asking in this set, the world number one converts.
A long, long way back now for Keys.
Bouchard out of Vinci match
News from the locker room and Eugenie Bouchard has had to pull out her singles match against Roberta Vinci later tonight as she continues to struggle with concussion after a locker-room slip.
Post update
Serena 6-3 3-3 Keys*
Serena Williams whips up 40-0 on the scoreboard with the speed and effeciency of Mary Berry on meringue duty.
Madison Keys shows a little mongrel as she produce a superb backhand punch down the line that leaves Williams leaning on her racquet like a walking stick.
But she can't make any more of 40-30. Serena holds.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Madison is keeping Serena guessing, got her thinking more on the return, which is exactly what she needed."
Post update
*Serena 6-3 2-3 Keys
After seeing off break points in her first two service games of the second set, Madison Keys breezes through to love.
A little bit more muscle and nous behind that tee-off? Williams regathering her forces for a tilt at the Keys serve at a later point?
We shall see.
Post update
Serena 6-3 2-2 Keys*
Serena Williams has been filling the gossip columns as well as the sport pages of the American media as she has apparently been getting to know Canadian music-maker Drake a little better.
No changes in the relationship status out on court in Arthur Ashe. It is still Williams in charge and Keys game, but inferior.
Serena batters her way to a hold for 15.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Lindsay Davenport gets so involved in these matches, we've seen a lot of emotion from her during Madison's career. It's way more stressful being a coach."
Keys holds after four break points
*Serena 6-3 1-2 Keys
EPACopyright: EPA
Serena Williams wants this done with Venus-style speed.
She flattens a mighty cross-court forehand to bring up 15-40 and two break points.
Keys under the magnifying glass like an ant at the mercy of a sadistic schoolboy.
First serve missed. Oh, a second serve ace! Keys brilliantly double-bluffing Williams as she goes to the world number one's favoured forehand wing and catches her wrong-footed.
Williams duffs a backhand long on the second.
Keys saves a third break point from deuce and then sees Williams twang the wire on a fourth and the ball loop agonisingly into the air...and just wide.
Keys' coach Lindsay Davenport is being put through the mincer by this game. Her girl has done the business though, finally sneaking home unscathed.
Post update
Serena 6-3 1-1 Keys*
Serena Williams chucks down her fourth and fifth aces of the match as she continued the sterling silver standard of service that she delivers at her best.
Keys with one point from the game, but that is only worth a little encouragement to her rather than scoreboard currency.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Great hold from Madison. You always want to win the first game of a set if you have lost the previous one, just to get some momentum back."
Keys saves break points to hold
*Serena 6-3 0-1 Keys
Serena Williams can coast her way into trouble at times, letting her opponents back into matches and invariably then crushing their rebellion just before it gathers any decisive momentum.
That does not look to be the case this time.
Serena climbs into a forehand return at deuce to bring up break point. Keys' serve under fire immediately at the start of the second set and she saves with a bold forehand right onto the outside half of the line.
That was gutsy. More thumping forehands, deep and accurate, get Keys out of the situation. That was big for the underdog and full credit for staying true to her strengths rather than playing safe when she teetered on the precipice.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"From the very first point, Serena has been the most focused I have seen her this year. She knows what Madison is capable of, so she came out determined to make a statement, which she has."
Game and first set
Serena 6-3 Keys*
Serena Williams has been cyborg serene as she goes about her business today.
The American is apparently locked in on the first set at 30-15 up, but then throws up an inexplicable error, planting an easy put-away into the top of the net with Keys having already given up on the point.
30-30. Keys pushing hard in the rally, finding the back corners and asking questions. But Serena keeps fetching and then throws the switch, upping the aggression, finding the angle and stretching Keys beyond her limits.
They were the two key points and Williams bags the first set.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Madison had been serving well, but that was a really weak service game. It happened because of how aggressive Serena has been on the Keys second serve."
Williams breaks
*Serena 5-3 Keys
EPACopyright: EPA
Now then. Serena Williams has a sniff at 15-30 and suddenly the hunt is on.
Madison Keys is under the pump and cracks as she duffs a second serve just long. Her error confirmed by the Hawk-Eye review.
15-40 and two break points. Keys misses with her first serve, Serena is straining on the leash to get at her second and when it comes a crunching return seals the break.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
ReutersCopyright: Reuters
"Both players are holding really easily. After the next couple of games, we'll start to see if they can keep holding to get to that tie-break."
Post update
Serena 4-3 Keys*
They won't be able to sell this set of balls to the punters after the match is done.
They are going to be more bruised than a banana in the bottom of a school bag.
Serena Williams holds to love, swatting away a smash on the final point.
Post update
*Serena 3-3 Keys
Madison Keys keeps the big-serving trend running. A hold to 15 that I was slightly distracted from by pictures of Eugenie Bouchard arriving at Flushing Meadows.
It was proper rehabbing rock star stuff, big shades, hoodie pulled up and a entourage of minders.
The Canadian, who pulled out of the doubles after a dressing room slip, is due to play Roberta Vinci in the singles later today.
Post update
Serena 3-2 Keys*
This is a little bit like something from the days of Michael Stich andYevgeny Kafelnikov in the men's game.
Whopping great serves are snuffing out any sniff of a break. Rallies at a premium. Both players winning more than 80% of points behind their first serves.
Serena Williams is the latest to rattle through.
AFPCopyright: AFP
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Madison is trying to take a huge swing because she knows the power of Serena. She's always aggressive, but she's being even more aggressive. It's the only way she'll be able to beat Serena."
Post update
*Serena 2-2 Keys
Madison Keys' forehand wind up is like one of those great big Roman catapults.
You can see it cranking into life a mile off, but that doesn't mean you can dodge the impending destruction.
She hammers away a mid-court bounce to take the game to 15.
Post update
Serena 2-1 Keys*
Madison Keys is not going to be forced back into her shell.
She has come out fighting fire with fire on return, using the power of the Serena Williams serve rather than being cowed by it.
Big swinging replies to the Serena serves. It is a tactic that is going to churn out a lot of errors, but it is undoubtedly her best bet. She nibbles off two points in that service game before Serena makes it over the line.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Serena knows how good a player that Madison Keys is. It's no surprise that she come out in this way because she knows the threat she poses."
Post update
*Serena 1-1 Keys
Madison Keys guides her serve past a rather passive Serena with a bit to spare.
The world number one looked like she was using that game as a bit of sighter, cracking returns into the top of the net.
Lindsay Davensport is picked out in the crowd by the television cameras, having a bit of chuckle with a companion.
Post update
Serena 1-0 Keys*
Does anyone do psyche-out stares like Serena?
The world number one collects three balls from the ball boy, discards one, steps up to the oche and takes a long, hard look down the other end of the court before finally launching into her service action.
It was a look that said "you have been weighed, you have been measured, and you have been found wanting".
The action that follows backs up the pre-point mood music.
Serena holds for the loss of a point, crashing down with a big bolshy ace at 4-15.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
Quote Message: At Wimbledon, any time someone mentioned the calendar Slam, Serena was saying 'don't talk about it'. That shows it was on her mind.
At Wimbledon, any time someone mentioned the calendar Slam, Serena was saying 'don't talk about it'. That shows it was on her mind.
S.Williams v Keys
Serena Williams, still zipped into a white tracksuit top, gets down a sneaky couple of extra serves as the umpire calls time on the warm-up.
Serena to serve.
Venus awaits
GettyCopyright: Getty
Serena Williams is on court a little earlier than she might have expected.
And that is thanks to sister Venus who walloped Anett Kontaveit of Estonia 6-1 6-2 in 50 minutes in the previous match on the main stage.
The winner of Serena v Madison Keys will be next for Venus, who offered some nice words after her win.
She was asked what it was like to be part of the most public sibling rivalry in sport.
"Awesome," she replied simply.
"I'm so proud of Serena and I think she is proud of me."
"Keep having fun"
The players are on court.
But not before lobbing up a few platitudes to an interviewer lurking in the bowels of the Arthur Ashe Stadium.
Serena Williams sounds a little nervous as she unclamps the headphones from the side of her head to answer.
"She has a lot of power, I have to be relaxed and calm and keep having fun," she says.
Getty ImagesCopyright: Getty Images
Super coach
GettyCopyright: Getty
Madison Keys has a good woman in her corner for this match.
Coach Lindsay Davenport had her own tangles with Serena at the tailend of her career and chalked up four wins from 14 meetings including one in the quarter-finals of the 2000 US Open.
Keys looked in pretty smart form in the last round, dismissing Agnieszka Radwanska 6-3 6-2.
Keys to victory?
Getty ImagesCopyright: Getty Images
Madison Keys is the next woman in the path of the Serena juggernaut.
The 20-year-old is the most promising of the new generation of American players and is unlikely to be a rabbit in the headlights.
She is one of the few players who can match Serena's groundstroke power and went toe-to-toe with the world number one in the first set of their Australian Open semi-final before folding 7-6 (7-5) 6-2.
Serena in numbers
Getty ImagesCopyright: Getty Images
Forget superlatives and poetry, just look at the brutal, raw numbers of Serena Williams' iron grip on the women's game.
She has won her last 31 matches in Grand Slams, and her last 24 at the US Open.
She has racked up 51 victories, five WTA titles and just two defeats in 2015.
She has twice as many ranking points as world number two Simona Halep.
And, of course, she has won all three Grand Slams this year.
She is just four wins from that calendar-year clean-sweep full house.
Live Reporting
Mike Henson
All times stated are UK
Get involved
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Getty ImagesCopyright: Getty Images 
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EPACopyright: EPA 
ReutersCopyright: Reuters 
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GettyCopyright: Getty 
Getty ImagesCopyright: Getty Images 
GettyCopyright: Getty 
Getty ImagesCopyright: Getty Images 
Getty ImagesCopyright: Getty Images
Latest PostPost update
Right, this live text, like Madison Keys, is heading out home after a creditable performance.
Just a reminder that the schedule is out for tomorrow.
Andy Murray v Kevin Anderson at approximate 19:30 BST and Jo Konta has got a prime-time slot, taking on BBC Sport columnist and two-time Wimbledon champion Petra Kvitova in the first match of the night session.
That gets going at midnight tomorrow.
Bye for now.
Post update
The match stats actually tell quite an interesting story.
Madison Keys hit more winners, 24 to Serena's 18, but really suffered on second serve, losing 18 of her 28 points off that shot.
Post update
Serena Williams, speaking on court: "It was really important to get a good start. Madison is so powerful and knows how to win big matches. My only chance was to start fast.
"I stayed in there and did the best I could. I relaxed, got a few lucky shots and got the break.
"My serve was much better today. I had to, because Madison has a great serve.
"I don't feel any pressure. Winning four in a row at Wimbledon was amazing. Now I have a chance here to make it five and the New York crowd is pushing me on. It makes me want to to perform and do better.
"The only difference to playing Venus now is that we're a lot older. She's playing great. I have to really be ready for her. At least one of us will be in the semis."
Post update
Serena Williams tells the on-court interviewer that she doesn't feel any pressure over the calendar Grand Slam, having bagged the Serena Slam (holding all four Grand Slam title, but not having actually won them all in the same year) at Wimbledon.
Full quotes on the way as Serena blasts a trio of signed balls to the cheap seats.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"What an impressive match from Serena. She served really well."
Game, set and match
Serena 6-3 6-3 Keys
Serena Williams, Lady Luck and service gremlins are all conspiring against Madison Keys as she folds out of the match as a fluky net cord goes against her and she then double-fault on the world number one's first match point.
Cue a curtsying and pirouetting Serena in the centre of Arthur Ashe.
Post update
Post update
Serena 6-3 5-3 Keys
Serena Williams is still crushing the ball and, if anything, is accelerating for home.
She brings up 40-0 in a twinkle and, although Madison Keys lobs a screwdriver in her gears momentarily with a superb forehand winner, Williams closes out with an ace on the next point.
Williams breaks
*Serena 6-3 4-3 Keys
After purring for most of the match, Madison Keys' game suddenly comes apart like a clown car.
The American duffs long with a squeal of dismay to hand Serena Williams a break point at deuce and, at the sixth time of asking in this set, the world number one converts.
A long, long way back now for Keys.
Bouchard out of Vinci match
News from the locker room and Eugenie Bouchard has had to pull out her singles match against Roberta Vinci later tonight as she continues to struggle with concussion after a locker-room slip.
Post update
Serena 6-3 3-3 Keys*
Serena Williams whips up 40-0 on the scoreboard with the speed and effeciency of Mary Berry on meringue duty.
Madison Keys shows a little mongrel as she produce a superb backhand punch down the line that leaves Williams leaning on her racquet like a walking stick.
But she can't make any more of 40-30. Serena holds.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Madison is keeping Serena guessing, got her thinking more on the return, which is exactly what she needed."
Post update
*Serena 6-3 2-3 Keys
After seeing off break points in her first two service games of the second set, Madison Keys breezes through to love.
A little bit more muscle and nous behind that tee-off? Williams regathering her forces for a tilt at the Keys serve at a later point?
We shall see.
Post update
Serena 6-3 2-2 Keys*
Serena Williams has been filling the gossip columns as well as the sport pages of the American media as she has apparently been getting to know Canadian music-maker Drake a little better.
No changes in the relationship status out on court in Arthur Ashe. It is still Williams in charge and Keys game, but inferior.
Serena batters her way to a hold for 15.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Lindsay Davenport gets so involved in these matches, we've seen a lot of emotion from her during Madison's career. It's way more stressful being a coach."
Keys holds after four break points
*Serena 6-3 1-2 Keys
Serena Williams wants this done with Venus-style speed.
She flattens a mighty cross-court forehand to bring up 15-40 and two break points.
Keys under the magnifying glass like an ant at the mercy of a sadistic schoolboy.
First serve missed. Oh, a second serve ace! Keys brilliantly double-bluffing Williams as she goes to the world number one's favoured forehand wing and catches her wrong-footed.
Williams duffs a backhand long on the second.
Keys saves a third break point from deuce and then sees Williams twang the wire on a fourth and the ball loop agonisingly into the air...and just wide.
Keys' coach Lindsay Davenport is being put through the mincer by this game. Her girl has done the business though, finally sneaking home unscathed.
Post update
Serena 6-3 1-1 Keys*
Serena Williams chucks down her fourth and fifth aces of the match as she continued the sterling silver standard of service that she delivers at her best.
Keys with one point from the game, but that is only worth a little encouragement to her rather than scoreboard currency.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Great hold from Madison. You always want to win the first game of a set if you have lost the previous one, just to get some momentum back."
Keys saves break points to hold
*Serena 6-3 0-1 Keys
Serena Williams can coast her way into trouble at times, letting her opponents back into matches and invariably then crushing their rebellion just before it gathers any decisive momentum.
That does not look to be the case this time.
Serena climbs into a forehand return at deuce to bring up break point. Keys' serve under fire immediately at the start of the second set and she saves with a bold forehand right onto the outside half of the line.
That was gutsy. More thumping forehands, deep and accurate, get Keys out of the situation. That was big for the underdog and full credit for staying true to her strengths rather than playing safe when she teetered on the precipice.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"From the very first point, Serena has been the most focused I have seen her this year. She knows what Madison is capable of, so she came out determined to make a statement, which she has."
Game and first set
Serena 6-3 Keys*
Serena Williams has been cyborg serene as she goes about her business today.
The American is apparently locked in on the first set at 30-15 up, but then throws up an inexplicable error, planting an easy put-away into the top of the net with Keys having already given up on the point.
30-30. Keys pushing hard in the rally, finding the back corners and asking questions. But Serena keeps fetching and then throws the switch, upping the aggression, finding the angle and stretching Keys beyond her limits.
They were the two key points and Williams bags the first set.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Madison had been serving well, but that was a really weak service game. It happened because of how aggressive Serena has been on the Keys second serve."
Williams breaks
*Serena 5-3 Keys
Now then. Serena Williams has a sniff at 15-30 and suddenly the hunt is on.
Madison Keys is under the pump and cracks as she duffs a second serve just long. Her error confirmed by the Hawk-Eye review.
15-40 and two break points. Keys misses with her first serve, Serena is straining on the leash to get at her second and when it comes a crunching return seals the break.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Both players are holding really easily. After the next couple of games, we'll start to see if they can keep holding to get to that tie-break."
Post update
Serena 4-3 Keys*
They won't be able to sell this set of balls to the punters after the match is done.
They are going to be more bruised than a banana in the bottom of a school bag.
Serena Williams holds to love, swatting away a smash on the final point.
Post update
*Serena 3-3 Keys
Madison Keys keeps the big-serving trend running. A hold to 15 that I was slightly distracted from by pictures of Eugenie Bouchard arriving at Flushing Meadows.
It was proper rehabbing rock star stuff, big shades, hoodie pulled up and a entourage of minders.
The Canadian, who pulled out of the doubles after a dressing room slip, is due to play Roberta Vinci in the singles later today.
Post update
Serena 3-2 Keys*
This is a little bit like something from the days of Michael Stich andYevgeny Kafelnikov in the men's game.
Whopping great serves are snuffing out any sniff of a break. Rallies at a premium. Both players winning more than 80% of points behind their first serves.
Serena Williams is the latest to rattle through.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Madison is trying to take a huge swing because she knows the power of Serena. She's always aggressive, but she's being even more aggressive. It's the only way she'll be able to beat Serena."
Post update
*Serena 2-2 Keys
Madison Keys' forehand wind up is like one of those great big Roman catapults.
You can see it cranking into life a mile off, but that doesn't mean you can dodge the impending destruction.
She hammers away a mid-court bounce to take the game to 15.
Post update
Serena 2-1 Keys*
Madison Keys is not going to be forced back into her shell.
She has come out fighting fire with fire on return, using the power of the Serena Williams serve rather than being cowed by it.
Big swinging replies to the Serena serves. It is a tactic that is going to churn out a lot of errors, but it is undoubtedly her best bet. She nibbles off two points in that service game before Serena makes it over the line.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
"Serena knows how good a player that Madison Keys is. It's no surprise that she come out in this way because she knows the threat she poses."
Post update
*Serena 1-1 Keys
Madison Keys guides her serve past a rather passive Serena with a bit to spare.
The world number one looked like she was using that game as a bit of sighter, cracking returns into the top of the net.
Lindsay Davensport is picked out in the crowd by the television cameras, having a bit of chuckle with a companion.
Post update
Serena 1-0 Keys*
Does anyone do psyche-out stares like Serena?
The world number one collects three balls from the ball boy, discards one, steps up to the oche and takes a long, hard look down the other end of the court before finally launching into her service action.
It was a look that said "you have been weighed, you have been measured, and you have been found wanting".
The action that follows backs up the pre-point mood music.
Serena holds for the loss of a point, crashing down with a big bolshy ace at 4-15.
Post update
Jill Craybas
Former world number 39 on BBC Radio 5 live sports extra
S.Williams v Keys
Serena Williams, still zipped into a white tracksuit top, gets down a sneaky couple of extra serves as the umpire calls time on the warm-up.
Serena to serve.
Venus awaits
Serena Williams is on court a little earlier than she might have expected.
And that is thanks to sister Venus who walloped Anett Kontaveit of Estonia 6-1 6-2 in 50 minutes in the previous match on the main stage.
The winner of Serena v Madison Keys will be next for Venus, who offered some nice words after her win.
She was asked what it was like to be part of the most public sibling rivalry in sport.
"Awesome," she replied simply.
"I'm so proud of Serena and I think she is proud of me."
"Keep having fun"
The players are on court.
But not before lobbing up a few platitudes to an interviewer lurking in the bowels of the Arthur Ashe Stadium.
Serena Williams sounds a little nervous as she unclamps the headphones from the side of her head to answer.
"She has a lot of power, I have to be relaxed and calm and keep having fun," she says.
Super coach
Madison Keys has a good woman in her corner for this match.
Coach Lindsay Davenport had her own tangles with Serena at the tailend of her career and chalked up four wins from 14 meetings including one in the quarter-finals of the 2000 US Open.
Keys looked in pretty smart form in the last round, dismissing Agnieszka Radwanska 6-3 6-2.
Keys to victory?
Madison Keys is the next woman in the path of the Serena juggernaut.
The 20-year-old is the most promising of the new generation of American players and is unlikely to be a rabbit in the headlights.
She is one of the few players who can match Serena's groundstroke power and went toe-to-toe with the world number one in the first set of their Australian Open semi-final before folding 7-6 (7-5) 6-2.
Serena in numbers
Forget superlatives and poetry, just look at the brutal, raw numbers of Serena Williams' iron grip on the women's game.
She has won her last 31 matches in Grand Slams, and her last 24 at the US Open.
She has racked up 51 victories, five WTA titles and just two defeats in 2015.
She has twice as many ranking points as world number two Simona Halep.
And, of course, she has won all three Grand Slams this year.
She is just four wins from that calendar-year clean-sweep full house.