Postpublished at 22:01 BST
So...mixed results for the Brits so far with a win for Toby Samuel and defeat for Cameron Norrie. Let's see how Katie Boulter gets on now.
She's up next on court five, followed by fellow Brit Jacob Fearnley.
Day one of the US Open in New York - listen to live commentary on BBC 5 Sports Extra (UK only)
Coming up: Katie Boulter opens against American wildcard Carol Young Suh Lee
Qualifier Toby Samuel beats Tomas Machac 6-2 6-3 6-2 on New York debut for first Grand Slam match win
But 29th seed Cameron Norrie loses 6-7 (6-8) 6-2 6-2 6-3 to Luca Van Assche
Lucky loser Jacob Fearnley rounds out play against Spain's Martin Landaluce
Third seed Jessica Pegula breezes through, 2021 champion Daniil Medvedev wins on Arthur Ashe Stadium
Harry Poole, Elizabeth Botcherby, Emily Salley and Melissa Edwards
So...mixed results for the Brits so far with a win for Toby Samuel and defeat for Cameron Norrie. Let's see how Katie Boulter gets on now.
She's up next on court five, followed by fellow Brit Jacob Fearnley.
Norrie 7-6 (8-6) 2-6 2-6 3-6 Van Assche
Pat Cash
Former Wimbledon champion on BBC Radio 5 Live
That very last point sort of summed up the match - just a very good solid first serve, got into a rally, nice opportunity short ball for Norrie and he just missed it. Time and time and time again it just wasn't a Cam Norrie performance.
In many ways he set the point up beautifully but it was just one of those days where you can't finish it off.
It wasn't a technical match Norrie would have been worried about, you have got to execute. Van Assche has played a lot of matches of late and he was just rock solid.
Samuel 6-2 6-3 6-2 Machac
This is Toby Samuel's first main-draw win at a Grand Slam.
The 23-year-old, who began this year ranked outside the world's top 250, came from a set down in each of his three qualifying matches to get here but had no such issues today against Tomas Machac.
Waiting for him in round two is another Czech in 18th seed Jiri Lehecka, who beat Pablo Carreno Busta in four sets.
Norrie 7-6 (8-6) 2-6 2-6 3-6 Van Assche
Luca Van Assche is through to the US Open second round for the first time!
An excellent display from the 22-year-old, you have to say.
Potentially there was something not quite right for Cameron Norrie, who fell away after winning the opening set.
The British number one, the 29th seed here in New York, is out.
Image source, Getty ImagesSamuel 6-2 6-3 6-2 Machac
Tomas Machac saves the first match point with a smashed winner but produces a forehand error on the second.
British qualifier Toby Samuel is through to the second round on his US Open debut.
Image source, Getty ImagesNorrie 7-6 (8-6) 2-6 2-6 3-5 Van Assche*
Long from Cam Norrie.
Match point, Luca Van Assche.
Norrie 7-6 (8-6) 2-6 2-6 3-5 Van Assche*
Pat Cash
Former Wimbledon champion on BBC Radio 5 Live
There was nothing on about five of those forehands from Van Assche in that last game but, such is Norrie's confidence, he's just missing those type of shots. The balls that are bouncing mid-court and shoulder height, his bread and butter if he was in form.
Norrie 7-6 (8-6) 2-6 2-6 3-5 Van Assche*
What has Cam Norrie got left here?
He's shown great spirit to keep in touch with Luca Van Assche, but he has been outplayed since the first set.
The Briton lets out another huge yell after levelling at 15-15, and has hope after his opponent double-faults for 30-30.
*Samuel 6-2 6-3 5-2 Machac
Tomas Machac gifts a couple more points away to present Toby Samuel with two match points.
Image source, Getty ImagesNorrie 7-6 (8-6) 2-6 2-6 3-5 Van Assche*
Cameron Norrie is getting himself fired up for the fight here, letting out a big roar as he moves to game point after Luca Van Assche reached deuce.
The Frenchman responds with a fizzing forehand into the back corner to haul Norrie back, though, and the still-quiet Van Assche shakes his fist after watching his opponent blast wide.
Norrie is the first to blink in an extended baseline exchange, and it leaves Van Assche a game away.
*Samuel 6-2 6-3 5-2 Machac
Shanked forehand. Tomas Machac led 2-0 in the third set. He's now trailing 5-2, with Toby Samuel - on his US Open debut - serving for a spot in the second round.
Samuel 6-2 6-3 4-2 Machac*
Tomas Machac is his own worst enemy. At 30-all, he gets down low to cushion a drop shot... and pops the ball in the net.
Samuel 6-2 6-3 4-2 Machac*
Two break points saved, five deuces navigated. Toby Samuel extends his lead. Phew.
*Samuel 6-2 6-3 3-2 Machac
Toby Samuel is on the back foot, defending for all he's worth as Tomas Machac - with a second break point - pummels deep return after deep return. But his resistance pays off, with the Czech eventually losing his composure and posting a forehand long.
*Norrie 7-6 (8-6) 2-6 2-6 3-4 Van Assche
Luca Van Assche dusts himself down after the disappointment of losing his advantage in this set and gets back on track with a hold to love.
Just two more games needed as far as the Frenchman is concerned - but Cameron Norrie has shown in the past few minutes that he still has enough to ensure it is not quite that simple.
*Samuel 6-2 6-3 3-2 Machac
Tomas Machac isn't going down without a fight. He recovers from 30-0 down to force deuce, unleashing a tracer bullet forehand with Toby Samuel on game point.
He couldn't capitalise on his break point but he's forced a fourth deuce on Samuel's serve, firing a cross-court backhand winner with the Briton rushing the net.
Norrie 7-6 (8-6) 2-6 2-6 3-3 Van Assche*
The shouts of "allez" have returned on Cameron Norrie's side of the court.
There's a spring in his step and he's making his winners now, lifting a lob over Luca Van Assche to level the fourth set at three games apiece.
*Norrie 7-6 (8-6) 2-6 2-6 2-3 Van Assche
It's a funny old game.
One minute Cameron Norrie's race appeared to be run, the next Luca Van Assche's level suddenly drops and the Briton is back in the set.
Still, there is a lot of work to do here.
Image source, Getty Images*Samuel 6-2 6-3 3-2 Machac
Tomas Machac pulls one point back but then fires an uncontrolled forehand well into the tramlines.
From 2-0 down, it's all looking quite rosy again for Toby Samuel. Big service game coming up to consolidate the break.
Norrie 7-6 (8-6) 2-6 2-6 1-3 Van Assche*
Oh, hold on a minute!
I don't think anyone sat around the court expected this game from Luca Van Assche. A double fault gifts Cameron Norrie two break points and a huge lifeline here.