French Open: Italian qualifier Martina Trevisan, ranked 159, had not won a Grand Slam main draw match before this tournament.
Simona Halep feels that travelling from Europe for the US Open will be tough as there are no direct flights.
The ATP and WTA tours are both suspended until late July due to the global health crisis.
Virtual Madrid Open: Andy Murray downed Belgium's David Goffin in the final but the drama of the online tournament took place in the previous round.
Naomi Osaka came from a break down in the third set to overcome Greece's Maria Sakkari in the first round of the WTA Brisbane International.
Ashleigh Barty and Belinda Bencic both advanced to the semi-finals after contrasting victories at the WTA Finals in China.
WTA Finals: Kiki Bertens won 3-6, 6-3, 6-4 in two hours and nine minutes in a see-saw match featuring 12 breaks of serve.
Naomi Osaka, who retired during last year's edition of the WTA Finals with a hamstring injury, had been due to play World No.1 Ashleigh Barty later on Tuesday.
Naomi Osaka was due to meet Madrid Open champion and sixth seed Kiki Bertens for a place in the final four of Italian Open.
Roger Federer admitted he struggled to get past the talented Gael Monfils.
Kiki Bertens fired eight aces to prevail 7-6 (7/2), 6-4 in one hour 43 minutes to record her first ever win over Donna Vekic.
Svitolina has looked on a mission at the WTA Finals in an effort to make amends for a lackluster early exit last year.
Naomi Osaka's WTA Finals debut ended in tears on Friday as she was forced to retire against Kiki Bertens.
By virtue of this win, Kiki Bertens secured her third WTA Tour singles title of the season.
Kiki Bertens defeated the world number one Simona Halep 2-6, 7-6 (8/6), 6-2 in the Cincinnati WTA final.
Kiki Bertens, who reached the French Open semi-finals in 2016, had never before been past the Wimbledon third round.
Petra Kvitova, the defending champion, dropped just one point on serve and stormed past Kiki Bertens into the second round.