Iga Swiatek believes she is growing into the US Open and improving with each day that passes after storming into the quarter-finals by beating Liudmila Samsonova.

Five-time grand slam winner Swiatek is hunting her second title at Flushing Meadows, and she will face home favourite Jessica Pegula in the last eight after overcoming Samsonova 6-4 6-1.

She needed just over an hour and a half to see off the 16th seed on Monday in what represented her 100th main-draw match at grand slams.

Among those to begin their careers in the Open Era, only six female players have bettered Swiatek's total of 83 victories through their first 100 major outings.

Monica Seles managed 93 wins, putting her ahead of Chris Evert (90), Steffi Graf (87), Martina Hingis, Serena Williams (both 86) and Venus Williams (85).

Swiatek is also one of just four players in the last two decades to win 12 straight grand slam matches versus WTA top-20 opponents, alongside Graf, Seles and Serena Williams.

She still believes there is more to come, though, as she approaches Tuesday's headline tussle with sixth seed Pegula.

"At the beginning, I felt like we were playing men's style, just holding our serves but I knew that if I kept pushing I may get some chances to break," Swiatek said. 

"That happened and I'm happy I was there to close the first set. Then I just wanted to keep being focused and not let my mind drift off.

"I'm happy with the whole performance. I'm feeling better and better every day."

The victor of Swiatek's meeting with Pegula will face Karolina Muchova or Beatriz Haddad Maia for a place in the final, after the former upset Jasmine Paolini and the latter overcame Caroline Wozniacki.

Haddad Maia's' 6-2 3-6 6-3 win over Wozniacki – who won the 2018 Australian Open – made her just the second South American woman to claim multiple US Open victories over former grand slam winners (two), alongside Argentina's Gabriela Sabatini.

Coco Gauff booked her place in the French Open fourth round after seeing off Dayana Yastremska in straight sets at Roland-Garros.

The third seed is still yet to drop a set in her opening three matches, as she battled past her Ukrainian opponent 32 6-2 6-4 in 94 minutes on Court Philippe-Chatrier.

Gauff's return game proved crucial against the 30th seed, who reached the Australian Open semi-finals as a qualifier back in January.

Indeed, the 2022 finalist won five of Yastremska's nine service games - taking her tally to 15-25 for the tournament - including two during a dominant opening set.

Another three followed in the second to put her on the brink of victory at 5-2 up, though she failed to convert match point as her opponent clung on to break back.

However, it proved a false dawn for the world number 30 - appearing in round three at Roland-Garros for the first time - as Gauff saved break points on her next service game to eventually hold and progress.

Her reward is a showdown with Elisabetta Cocciaretto, who will make her maiden fourth-round appearance at a major after defeating 17th seed Liudmila Samsonova 7-6 (7-4) 6-2.

Data Debrief: Gauff matches Capriati at Roland-Garros

Gauff is only the second American in the Open Era to reach the last 16 at the French Open in four successive years before turning 21, after Jennifer Capriati (1990 to 1993).

That was also her 18th match win at Roland-Garros. Since 2000, only Iga Swiatek (21) and Ana Ivanovic (19) have registered more before the age of 21.

Her fourth-round opponent has made history, with 23-year-old Cocciaretto the youngest Italian to reach the fourth round here since Francesca Schiavone in 2001.

Naomi Osaka was knocked out of the Madrid Open by Liudmila Samsonova after an entertaining second-round battle on Thursday.

Having won her first match on clay for two years against Greet Minnen a day earlier, Osaka was able to force a final set against 15th seed Samsonova but ultimately fell to defeat.

Samsonova won a close encounter 6-2 4-6 7-5 to book a clash with American Madison Keys – who defeated Irina-Camelia Begu in straight sets – in the next round.

Osaka had beaten Samsonova at Indian Wells last month and came close to securing another victory as she recovered well from losing the opening set.

But the Japanese star was broken to fall 5-6 behind in the final set, and the Russian made no mistake in ruthlessly closing out the victory.

Data Debrief: Samsonova ends losing streak

This was a crucial win for Samsonova, who came into the match having lost four consecutive contests, including that Indian Wells defeat to Osaka on March 9.

Samsonova did apply plenty of pressure in the final set – forcing five break points compared to just one for Osaka – and was ultimately rewarded in the closing stages of a contest that lasted two hours and 22 minutes.

Naomi Osaka comprehensively dispatched Greet Minnen on Tuesday to make a winning start to her Madrid Open campaign and earn a first win on clay for two years.

Japanese star Osaka triumphed 6-4 6-1 in only 79 minutes, swiftly booking a second-round clash against Liudmila Samsonova.

Osaka reached the last 32 at the WTA 1000 events on the hard courts of Indian Wells and Miami but had lost to Martina Trevisan at the first hurdle in the Open de Rouen on clay at WTA 250 level last week.

This was therefore a welcome return to form against Belgian qualifier Minnen and represented her first triumph on the surface since beating Anastasia Potapova at this tournament in 2022.

After an even start to the contest, the first set was level at 4-4. But Osaka then assumed full control, winning eight of nine games to race to victory.

Data Debrief: Osaka dominates on serve

Osaka was not broken at all in the match and allowed Minnen only one break-point opportunity across the whole contest.

She fired down eight aces to only three double faults, and won 13 of her 16 first-serve points in the second set.

Paula Badosa believes she can break back into the world's top three after cruising past Daria Kasatkina at the Porsche Tennis Grand Prix, where Emma Raducanu crashed out on Tuesday.

Seventh seed Kasatkina had no answers in Stuttgart as she fell to a 6-1 6-1 defeat against Badosa, who recorded the ninth top-10 victory of her career and first in exactly 12 months.

Badosa has won 29 clay-court matches in the last three seasons – only Ons Jabeur (35) and Iga Swiatek (30) have won more – but the Spaniard had to enter this tournament as a wildcard.

The 25-year-old was as high as second in the world last year but has fallen to 31st, and she outlined her goal to reach the top once more after her first-round win set up an all-Spanish meeting with Cristina Bucsa.

When asked about her ambitions to return to the world's top three, Badosa said: "That's what I'm working on every day. That's one of my goals – I want to be back on the top.

"I like to play big matches, I like to be in the last rounds of the tournaments. I still know I have that level. I still know I was that player. I still believe in myself, and I hope I'm back there very soon."

Jelena Ostapenko eased into the second round with similar dominance after downing Raducanu 6-2 6-1 in just 58 minutes, teeing up a meeting with world number four Ons Jabeur on Wednesday.

Latvian Ostapenko powered 19 forehand winners and went unbroken, acknowledging in her on-court interview that familiar aggression was key to her success in the battle of two one-time grand slam winners.

"I knew against her the main thing was to step in the court," said former French Open winner Ostapenko. "I missed some balls, but I tried to be aggressive all the time when it was possible.

"Just try to take the ball early, don't give her many chances. And finally, I'm back on clay, my favourite surface."

Barbora Krejcikova was another straight-sets winner, scoring a 6-2 6-0 triumph over Liudmila Samsonova, with the reward for the 2021 Roland Garros champion being a tricky clash against second seed and Australian Open winner Aryna Sabalenka.

There was no such ease for Anastasia Potapova in a battling 6-3 3-6 7-6 (7-4) victory over Petra Martic, the Russian's ninth third-set win in 2023 – no WTA Tour player has managed more.

Tatjana Maria overcame Ylena In-Albon 6-2 4-6 7-6 (7-4) in another enticing clash, while Beatriz Haddad Maia advanced after Martina Trevisan was forced to retire when trailing 7-5 1-1 due to a right thigh injury.

Jessica Pegula and Coco Gauff headlined a great day for the Americans at the Miami Open as they both advanced into the third round on Thursday.

Pegula, who is the second-highest seed remaining in the field after Iga Swiatek's withdrawal, had no issue dispatching Canada's Katherine Sebov 6-3 6-1 in just 66 minutes.

Gauff, the six seed, followed suit as she raced to a 6-4 6-3 win over Canadian Rebecca Marino in just 73 minutes.

Florida's own Danielle Collins thrilled her hometown crowd with a 7-6 (7-3) 6-2 triumph against Bulgaria's Viktoriya Tomova, and rising 22-year-old talent Clare Liu made it a perfect 4-0 sweep for the USA representatives by defeating Julia Grabher 6-4 6-3.

Last week's Indian Wells Open champion Elena Rybakina was made to work in her 7-5 4-6 6-3 win over Anna Kalinskaya, while an even more gruelling effort was required in Paula Badosa's two-hour-and-52-minute 7-6 (7-2) 4-6 6-2 result against Laura Siegemund.

The top seed to fall on Thursday was eighth seed Daria Kasatkina, as she won the first set before going down 4-6 6-2 6-2 against Elise Mertens.

Liudmila Samsonova, the 12th seed, made light work of Viktorija Golubic in a 6-1 6-1 drubbing, and 22nd seed Jelena Ostapenko prevailed 6-3 6-4 against Mirjam Bjorklund.

Ostapenko will next play 13th seed Beatriz Haddad Maia after she won a strange back-and-forth contest 7-6 (7-4) 0-6 6-0 over Tereza Martincova.

Liudmila Samsonova progressed after a marathon battle at the Dubai Tennis Championships, while Petra Kvitova breezed through as the seeds escaped unscathed on Sunday.

Two-time Wimbledon champion Kvitova, the 12th favourite in the United Arab Emirates, eased past Italy's Martina Trevisan 6-2 6-1 to make a dominant start.

World number 15 Samsonova was made to work to beat Paula Badosa, winning 6-7 (3-7) 7-6 (7-5) 6-4 to tee up a clash with Qinwen Zheng, who overcame compatriot Zhang Shuai in straight sets.

Samsonova's triumph took three hours and 22 minutes, the longest match of the WTA Tour season thus far, in a thrilling first-round encounter between two top-20 players.

"Playing against Paula is always tough," 14th seed Samsonova said in her on-court interview. "She's doing unbelievable, so I'm really proud that I stayed on the court until the end.

"I think I'm growing match after match, day by day. I know it's a long journey, and I hope to continue like that."

Barbora Krejcikova, the 2021 French Open champion, cruised into the last 32 with a comfortable 6-4 6-2 victory over Irina-Camelia Begu as she aims to go one better than her runners-up finish two years ago in Dubai.

Another routine victory saw American Madison Keys ease past Jasmine Paolini 6-1 6-1, but there was no such luck for 2020 Australian Open champion Sofia Kenin.

She was dispatched 6-1 6-1 by world number 26 Marie Bouzkova, while Amanda Anisimova claimed a 6-3 6-2 win over veteran two-time grand slam finalist Vera Zvonareva.

Viktoriya Tomova had too much for Kaia Kanepi in a 6-3 6-1 success, with her reward a second-round clash against third seed Jessica Pegula.

World number four Pegula lost to the in-form Iga Swiatek in the Qatar Ladies Open final on Saturday, and Leylah Fernandez will face the Pole next after beating Julia Grabher 6-4 6-2.

Belinda Bencic claimed the inaugural Abu Dhabi Open title after saving three championship points in a gripping comeback win against Liudmila Samsonova.

Second seed Bencic did not drop a single set en route to Sunday's final, but she fell behind to Samsonova and was on the brink of defeat when 6-4 down in a second-set tie-break.

The Swiss dug deep to take the game to a decider, however, and she prevailed 1-6 7-6 (10-8) 6-4 in a time of two hours and 48 minutes to win the eighth WTA title of her career.

World number nine Bencic, who was also victorious at the Adelaide International 2 in January, made a slow start against an opponent she had failed to beat in three meetings.

Samsonova broke Bencic in the second and sixth games of the opening set in a dominant start as she looked to make it 5-0 in championship matches on the WTA Tour.

Bencic improved in the second set, although a break of serve apiece meant it went the distance.

Eighth seed Samsonova looked good value to wrap up a straight-sets win when 6-4 up, only for Bencic to save both championship points, and likewise at 8-7.

Three points in a row saw the 25-year-old take the tie and level up the contest, which she went on to win with a couple of breaks in the deciding set.

Belinda Bencic breezed through to the Abu Dhabi Open final after a commanding 6-2 6-3 victory over Beatriz Haddad Maia on Saturday.

The world number nine, who is yet to drop a set this week, is into her second WTA final of 2023, having triumphed in Adelaide last month.

Haddad Maia arrived in the clash fresh from winning each of her previous six encounters with top-10 opponents, including her quarter-final victory over Wimbledon champion and Australian Open finalist Elena Rybakina.

But the Brazilian had already spent almost eight hours on court in this event prior to this contest, in which Bencic dropped just five games on the way to wracking up her 11th win of the campaign – the joint-most on the WTA Tour alongside Melbourne winner Aryna Sabalenka.

She will play number eight seed Liudmila Samsonova in Sunday's final after the Russian defeated Zheng Qinwen 6-4 1-6 6-4.

After being edged out in the first set, Zheng responded to motor through the second and seemed to have the momentum going into the third, but Samsonova showed impressive resolve to see off three break points against her, before taking her first on match point.

At the Linz Open, top seed Maria Sakkari is out after going down 3-6 6-3 6-4 to sixth seed Petra Martic in a match that lasted over two and a half hours.

The Croatian will play Anastasia Potapova in the final after the number eight seed claimed yet another three-set victory this week to see off Marketa Vondrousova 6-1 6-7 (4-7) 6-3 and secure her fifth WTA final appearance.

Top seed Daria Kasatkina succumbed to a surprise quarter-final exit against Zheng Qinwen at the Abu Dhabi Open as Belinda Bencic marched into the final four.

Kasatkina was blown away in just 78 minutes by Zheng, who only dropped three games in her 6-1 6-2 upset of the world number eight.

Zheng, who defeated world number 12 Jelena Ostapenko on Wednesday, executed her serve-and-volley approach expertly throughout, with the 20-year-old claiming the third top-10 victory of her career to reach her third tour-level semi-final.

Another Russian player stands between Zheng and a place in the final after eighth seed Liudmila Samsonova dispatched compatriot Veronika Kudermetova 6-3 6-3.

Bencic found form after edging a tough first set against qualifier Shelby Rodgers, who saw her run ended by a 7-6 (7-5) 6-2 defeat.

Second seed Bencic will face Beatriz Haddad Maia in the semi-finals after the Brazilian railed to beat Elena Rybakina 3-6 6-3 6-2 less than 24 hours after beating Yulia Putintseva in a marathon three-hour encounter.

Meanwhile, top seed Maria Sakkari secured her progress to the last four at the Linz Open with a 6-3 7-6 (10-8) straight sets win over Donna Vekic.

The Greek will face off with Petra Martic next, while Anastasia Potapova faces the unseeded Marketa Vondrousova in the other semi-final.

Aryna Sabalenka secured a straight-sets win in her first match of 2023, but was made to work for it by Liudmila Samsonova at the Adelaide International.

The number two seed won 7-6 (10-8) 7-6 (7-3), saving seven set points after going 5-1 down in the first set, before roaring back to take both tie-breaks.

Sabalenka will face Marketa Vondrousova in the quarter-finals, with the Czech having produced a dominant performance in a 6-0 6-4 win against Kaia Kanepi. 

"When it's 1-5 down, it's like you have nothing to lose, and you just go for your shots without thinking," Sabalenka said.

"That really helped me to stay in the set, to keep fighting and to keep trying."

Fourth seed Veronika Kudermetova eased through after a 6-4 6-0 victory against Bianca Andreescu, while Marta Kostyuk also advanced with a hard-fought 6-7 (5-7) 6-2 6-3 win over Elena Rybakina.

At the ASB Classic in Auckland, second seed Sloane Stephens is out after falling to Rebeka Masarova.

Having been forced to resume on Wednesday after rain suspended play the previous day, Stephens struggled against her Spanish opponent, eventually losing 6-3 7-6 (7-5).

Fifth seed Wang Xiyu is also out after retiring from her match against Karolina Muchova, but seventh seed Danka Kovinic is through after a simple 6-1 6-4 win against Nao Hibino.

Kovinic will face Lauren Davis next after she overcame Tamara Zidansek 6-2 6-1, while fellow American Sofia Kenin will take on number one seed Coco Gauff in the last 16 after she beat Wang Xinyu in straight sets.

Linda Noskova produced the biggest win of her career as she defeated Daria Kasatkina 6-3 6-7 (2-7) 6-3 at the Adelaide International on Monday.

The 18-year-old Czech was impressive against the third seed as she recorded her first win against anyone in the top 30 of the world rankings.

Fourth seed Veronika Kudermetova eased past Amanda Anisimova in just an hour and 15 minutes, winning 6-3 6-0, while Liudmila Samsonova will face second seed Aryna Sabalenka in the next round after coming from a set down to beat Zhang Shuai 5-7 6-3 6-0.

Irina-Camelia Begu and Elena Rybakina also both came from behind to secure wins, with the latter beating fifth seed Danielle Collins to set up a last-16 clash against Ukrainian Marta Kostyuk, who beat Jaimee Fourlis 6-1 3-6 6-4.

At the ASB Classic in Auckland, 42-year-old Venus Williams comfortably overcame her 21-year-old opponent Katie Volynets 7-6 (7-4) 6-2, and will play China's Zhu Lin next after she eliminated sixth seed Madison Brengle 4-6 7-6 (8-6) 6-4.

Third seed Leylah Fernandez beat Brenda Fruhvirtova 6-1 6-1 to set up a last-16 tie with Julia Grabher after she defeated Tereza Martincova in three sets.

Eighth seed Rebecca Marino is through after beating Dalma Galfi in straight sets and will now face Ysaline Bonaventure, who eventually put away Caty McNally 5-7 6-4 6-4.

Viktoria Kuzmova led fourth seed Bernarda Pera 5-4 in the opening set when rain stopped play for the day.

Victoria Azarenka has booked a clash with the top seed of the Guadalajara Open after defeating Elina Avanesyan 6-4 6-2 in Monday's opening round.

In the last event of the season before the WTA Finals, Belarus' Azarenka was too strong with her return game for her Russian opponent, winning 53 per cent (32-of-60) of her return points while capitalising on five-of-seven break point opportunities to earn a shot at world number eight Paula Badosa.

While Azarenka has no chance of qualifying for the WTA Finals – with only the top-eight players in the rankings making it through – Belinda Bencic is one of the players who can sneak in with a great result this week.

Needing to make the semi-finals to have a chance, she got off on the right foot with a 7-5 6-7 (10-12) 6-3 win against Leylah Fernandez in her opening match.

Petra Kvitova can also qualify if she reaches the final, and she started without issue, defeating Bernarda Pera 6-3 7-5.

Ekaterina Alexandrova had an outside chance of claiming a WTA Finals spot if she won this tournament, but she was the victim of the day's biggest upset, falling 6-4 7-6 (10-8) to Camila Osorio.

At 22nd in the world, Liudmila Samsonova is the lowest-ranked player in the field with a mathematical chance at qualification, but she is a step closer after handling Kaia Kanepi 6-1 7-5.

Despite Fernandez's earlier loss, it was a strong day for the Canadians, with Bianca Andreescu proving too good in her 6-2 6-4 victory against Jil Teichmann, and Rebecca Marino also only needed two sets to defeat Ann Li 6-2 7-6 (7-2).

China's Lin Zhu came from a set behind to beat France's Alize Cornet 3-6 6-3 6-4, while Ukraine's Marta Kostyuk had a much quicker result in her 6-1 6-3 triumph over Belarus' Aliaksandra Sasnovich.

World number 34 Elise Mertens had no problems in one of the biggest mismatches of the day as she defeated world number 185 Asia Muhammad 6-3 6-2, and Sloane Stephens needed only 54 minutes to advance 6-0 6-2 past Linda Fruhvirtova.

In the last match of the night, Mexico's top chance Fernanda Contreras Gomez was eliminated by Alja Tomljanovic 6-2 6-1.

In a first-round clash between two of the world's top-20, Danielle Collins eliminated Caroline Garcia 6-2 7-6 (7-4) from the San Diego Open on Monday.

Garcia, the world number 10, entered the contest off back-to-back losses for the first time since March, and Collins made it three in a row as she was just a little too good with both her serving and return game.

Collins won 63 per cent of her service points, with Garcia at 52 per cent, and she ended up securing five breaks in the match.

She will play Martina Trevisan in the second round after the Italian defeated Colombian qualifier Camila Osorio 6-3 6-4.

Neither player had an ace in the match, but the big differentiating factor was Trevisan's ability to win points off her second serve, converting 50 per cent of her chances while Osorio won only one of nine (11 per cent).

The only qualifier of the day to get a win was Louisa Chirico, who beat fellow American Alison Riske-Amritraj 1-6 7-5 7-6 (7-5).

Chirico, the world number 196, will be rewarded for her win with a showdown against world number four Paula Badosa.

Madison Keys had no issues dealing with Australian qualifier Ellen Perez 6-1 6-4 in just over an hour, and Coco Vandeweghe defeated Sofia Kenin 6-1 1-6 6-4.

In the last match of the night, Canada's Bianca Andreescu won a two-hour-and-40-minute battle against Russia's Liudmila Samsonova 7-6 (7-1) 4-6 6-2.

Emma Raducanu was forced to retire from her Korea Open semi-final against Jelena Ostapenko due to injury, leaving the Latvian to face second seed Ekaterina Alexandrova in Sunday's final.

The 2021 US Open winner was featuring in her first semi-final since that fairytale triumph at Flushing Meadows, and took the opening set 6-4 after making a flying start on Saturday.

Ostapenko then fought back to level the match, with Raducanu first appearing to struggle with her movement when she was a break up in the second, forcing her to take an off-court medical timeout.

The 19-year old later retired citing a left glute injury when 3-0 down in the decider, ending her confidence-boosting run in Seoul and teeing up a final meeting between the top two seeds.

Indeed, Alexandrova enjoyed a more routine outing in her meeting with Wimbledon semi-finalist Tatjana Maria, downing the German 6-2 6-4 to advance to her second final of the year.

At the Pan Pacific Open in Tokyo, meanwhile, Chinese teenager Zheng Qinwen reached her first WTA Tour final with a hard-fought win over world number 13 Veronika Kudermetova.

Having required over three hours to seal her 5-7 6-3 7-6 (7-3) triumph, the world number 36 said: "After the match when I won the last point, the feeling was incredible. 

"The opponent, she's playing unbelievable tennis. She has a really good serve and hits the ball hard, she moves well. It's my first time in the final. I'm so happy."

Her compatriot Zhang Shuai was unable to replicate those exploits, however, as Liudmila Samsonova eased into her third WTA final of the year with a 7-6 (7-4) 6-2 win. 

In-form Samsonova has won both of her previous final appearances this year - each of which came last month - and is 3-0 in showpiece matches for her career.