Swiatek, the 2022 champion, made her intentions clear early on with an aggressive start to claim a break for a 2-1 lead. She pulled further away when Kostyuk hit a double fault two games later, wrapping up the opening set in 31 minutes.
Local favourite Thompson saved three match points before prevailing 5-7, 7-6 (6), 6-3 against Nadal, who was playing his first tournament after nearly a year out with a hip injury.
IMAGES from Day 7 of the Wimbledon Championships, at the All England Lawn Tennis and Croquet Club, London, on Sunday.
A true legend of the game who paved the way and taught so many of us how to be as a player and as a person.
Fourth seed Alexander Zverev will play Brandon Nakashima as the former finalist looks to end his long wait for a maiden Grand Slam title.
Swiatek made the most of Kasatkina's string of unforced errors, peppering court Philippe Chatrier with winners.
Iga Swiatek said she was "overwhelmed" after finding out Poland and Bayern Munich striker Robert Lewandowski was in attendance
Murray knocked out by Fritz in Washington
Swiatek is positioned to face American fourth seed Jessica Pegula in the semi-finals.
Images from Day 8 of the 2024 French Open at Roland Garros on Sunday.
Coco Gauff battled past Elina Svitolina in the Auckland Classic final on Sunday to retain her title.
Novak Djokovic beat 14-times French Open champion Rafael Nadal in straight sets at the Paris Olympics on Monday.
Images from Day 2 of the 2024 French Open at Roland Garros in Paris on Monday.
It was an emotional win for Aryna Sabalenka, who missed Wimbledon last month due to a shoulder injury.
IMAGES from Day 10 of the Australian Open in Melbourne on Tuesday.
Naomi Osaka's return a boost for women's tour, says Mouratoglou
IMAGES from Day 1 of the Wimbledon Championships, at the All England Lawn Tennis and Croquet Club, London, on Monday.
Images from the Olympics tennis action at the Roland Garros, Paris, on Wednesday.
Along with offering a trophy and spot in the tennis history books, the four Grand Slams also provide serious financial incentive for would-be champions.
'Meeting a real queen, that would be pretty cool'
Images from the US Open men's singles third round match at Flushing Meadows, New York, on Friday.
Holger Rune rallied from a set down and saved a match point to defeat former champion Taylor Fritz 2-6 7-6(2) 6-3 on Wednesday and reach the Indian Wells quarter-finals where he will meet fourth seed Daniil Medvedev.
Iga Swiatek, Aryna Sabalenka and Coco Gauff, are a handful of contenders ready to swoop in
Twice finalist Ruud overcomes Davidovich Fokina test
Italy's Matteo Arnaldi produced a sensational performance to take out sixth seed Andrey Rublev and reach the last 16 of the French Open on Friday.
A summary of the day's tennis action at Roland Garros.
Big-serving Elena Rybakina will aim to retain her title but other players have emerged as serious contenders:
Three contenders for the women's singles title at the Australian Open.
A frustrated Coco Gauff broke down in tears after her 7-5, 6-3 defeat by Jelena Ostapenko at the Australian Open on Sunday.
Caroline Garcia and Kristina Mladenovic recovered from a set down to beat Americans Coco Gauff and Jessica Pegula
Factbox on Belarus' Aryna Sabalenka, who beat China's Zheng Qinwen in the Australian Open final on Saturday
'I think this tournament was the first tournament this year that I went in trying to win for myself, and I think that was the difference in my mentality'
Hurkacz, Swiatek win as Poland march into United Cup final
After the women's doubles finalists weren't given the chance to speak at the trophy ceremony at the Madrid Open, the organisers apologised.
Photos pf tennis action across the USA on Sunday.
Gauff survives scare, Osaka advances
Swiatek is on a remarkable 34-match winning streak On the other side, Gauff has developed into a solid claycourt player
'I grew up watching her. That's the reason why I play tennis'
Novak Djokovic will prepare for a tilt at an 11th Australian Open title by representing Serbia at the United Cup mixed team tournament while old rival Rafael Nadal and former women's world number one Naomi Osaka return at Brisbane after time away.
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