Images from the US Open men's singles first round matches, at Flushing Meadows, New York, on Tuesday.
Rafael Nadal continued his perfect run on the North American hardcourts taming Czech Tomas Berdych 7-5, 7-6 (4) at the Western and Southern Open on Saturday to setup a final showdown with big-hitting American John Isner.
Heading into the final, Gauff had lost the first set in three straight matches and the former U.S. Open champion seemed determined to buck that trend, serving to love in the opening game and breaking early for a 2-0 lead.
Alcaraz, winner of the last two Grand Slams at Roland Garros and Wimbledon, had made it to at least the quarter-final stage at every major in which he has competed since winning the US Open two years ago.
Nick Kyrgios has been fined $113,000 by the ATP for arguing with the chair umpire and smashing two rackets during his second-round loss at the Cincinnati Masters.
World number one Dinara Safina will take on a rejuvenated Jelena Jankovic in the final of the Cincinnati Open after hugely contrasting wins on Saturday. Russian Safina stormed into her eighth final of the year with a 6-2, 6-0 demolition of Italian Flavia Pennetta, while fifth seed Jankovic saved four match points to beat fourth seed Elena Dementieva 7-6, 0-6, 7-6 after two hours and 46 minutes.
Serena Williams, coming off a double Olympic gold medal-winning performance in London, said she was feeling the pace of a hectic schedule after a lethargic display in her 6-3, 6-0 win over Urszula Radwanska on Thursday.
World number one Dinara Safina scrambled past Italian Roberta Vinci 2-6, 7-5, 6-4 to reach the third round of the Cincinnati Open on Tuesday. World number 46 Vinci served for the match at 5-4 in the second set but her nerve failed her at the crucial time.
Naomi Osaka has four major titles under her belt but the second round at Flushing Meadows, Wimbledon and Roland Garros was as good as it got this year for the Japanese 26-year-old, who exited the Australian Open in the first round.
Tiger-tattooed Aryna Sabalenka clawed her way back from injury and disappointment to hoist the US Open trophy at last.
The Indo-Czech duo advanced after fifth seeds Paul Hanley and Kevin Ullyet withdrew while trailing 3-5 in the first set.
The Cincinnati Open claimed two more high-profile victims on Thursday with Grand Slam champions Li Na and Petra Kvitova crashing out, while Russian pair Maria Sharapova and Vera Zvonareva crunched their opponents en route to the quarter-finals.
Mahesh Bhupathi and Jamie Murray fell to top seeds Mike and Bob Bryan in the second round.
Making her first semi-final appearance after quarter-final exits at each of the last two editions of the tournament, Sania confessed that she ran out of steam towards the end.
Rafael Nadal and Roger Federer, numbers two and three in the world, suffered surprise defeats to Mardy Fish and Tomas Berdych respectively in an entertaining quarter-finals day at the Cincinnati Open on Friday.
Novak Djokovic is returning to the US for the first time in two years after being denied entry due to being unvaccinated for COVID-19.
Sania Mirza was leading 6-1, 2-0 when Alexandra Stevenson retired with a right shoulder strain.
Britain's Andy Murray, who lost his Cincinnati Masters quarter-final to American Mardy Fish Friday, was disappointed that tournament organisers had given him three consecutive starts in the midday heat.
Carlos Alcaraz said he will be "at 100%" for the US Open despite stopping his training in New York on Saturday as a precaution after twisting his ankle.
Russia's Maria Sharapova beat Serbia's Jelena Jankovic 4-6, 7-6, 6-3 to win the Cincinnati Open on Sunday and install herself as one of the favourites for the US Open.
Sania Mirza, seeded ninth, advanced with a 6-1, 0-6, 6-1 victory over Finland's Emma Laine.
France's Gael Monfils and Gilles Simon suffered early exits from the Cincinnati Masters on Tuesday.
Kim Clijsters survived three match points before a rain break then produced a remarkable comeback after the weather cleared to beat Maria Sharapova 2-6, 7-6, 6-2 and win the Cincinnati Open on Sunday.
Mahesh Bhupathi and Max Mirnyi suffered their third defeat in an ATP Masters series final this season, losing the summit clash of the Cincinnati event 3-6, 4-6 to second seeds Mike and Bob Bryan.
Indian tennis ace Mahesh Bhupathi and his Belarussian partner Max Mirnyi reached their third ATP World Tour final of the year together, beating fifth seeds Lukasz Kubot and Oliver Marach in straight sets in the Cincinnati Masters Tennis Tournament.
Mahesh Bhupathi and Max Mirnyi booked a semi-final berth at the ATP Cincinnati Masters after sailing past Mariusz Fyrstenberg and Marcin Matkowski in straight sets in Mason, USA.
Leander Paes and the Czech Republic's Lukas Dlouhy stumbled yet again in the second round, crashing out of the Cincinnati Masters, following a straight-set defeat to Mardy Fish and Mark Knowles. Seeded third, they lost 3-6, 2-6 to the unseeded American-Bahamas pair.
World number one Rafa Nadal battled back to defeat Frenchman Julien Benneteau 5-7, 7-6, 6-2 at the Cincinnati Masters on Thursday and Britain's Andy Murray needed a final set tiebreak to beat Latvia's Ernests Gulbis.
Andy Roddick needed three sets to beat 46th-ranked Ukrainian Sergiy Stakhovsky 6-4, 6-7, 6-1, while fellow American Taylor Dent upset Feliciano Lopez to advance to the second round of the Cincinnati Masters on Monday.
Russia's Elena Dementieva lost 6-1, 6-3 to compatriot Anastasia Pavlyuchenkova in the second round of the rain-hit Cincinnati Open on Wednesday, but Maria Sharapova and Kim Clijsters both advanced to the third round.
Novak Djokovic, Andy Murray, Rafael Nadal and Roger Federer all picked up third round wins at the Western and Southern Open on Thursday to set up a star-studded last eight in Cincinnati.
She beat Kristina Brandi 7-6, 7-5 in the second round of the Western and Southern Financial Group Women's Open.
Mahesh Bhupathi and Rohan Bopanna had to be content with a runners-up finish at the ATP Cincinnati Masters as they lost the summit clash in straight sets to Sweden's Robert Lindstedt and Romania's Horia Tecau.
World number one Roger Federer warmed up for the defence of his U.S. Open title in perfect fashion as he beat fourth seed Novak Djokovic 6-1, 7-5 to win the Cincinnati Masters on Sunday.
A rejuvenated Jelena Jankovic upset world number one Dinara Safina 6-4, 6-2 to win the Cincinnati Open on Sunday. The fifth-seeded Serb took advantage of an error-strewn display from the Russian to clinch her second title of the year.
Mahesh Bhupathi and Rohan Bopanna have earned a chance to win their second title of the season by reaching the summit clash of the ATP Cincinnati Masters with a straight sets win over Croatia's Ivan Dodig and Brazil's Marcelo Melo.
Mahesh Bhupathi and Rohan Bopanna, who were omitted from India's Davis Cup team, have reached the semi-finals of the ATP Cincinnati Masters with a hard-earned win over third seeds Mariusz Fyrstenberg and Marcin Matkowski.
Olympic champion Andy Murray suffered a second pre-US Open setback in as many weeks when he was knocked out of the Cincinnati Open in the third round on Thursday, losing 6-4, 6-4 to France's Jeremy Chardy.