Barty advanced to the semi-finals of the WTA Finals with a straight-sets win over Kvitova, while Bencic progressed when Bertens retired.
Elina Svitolina beat Simona Halep in straight sets in confident style to book her place in the semi-finals at the WTA Finals in Shenzhen.
Belinda Bencic withstood a second-set fightback from Petra Kvitova to earn a vital win that keeps her in the running at the 2019 WTA Finals.
Belinda Bencic beat her good friend Donna Vekic in straight sets to advance to her first-ever Grand Slam semi-final at US Open 2019.
Elina Svitolina advanced to the semi-final of US Open 2019 after beating Johanna Konta in straight sets in a pulsating encounter.
Elina Svitolina earns revenge for her 2017 loss to Madison Keys at the US Open by beating her in straight sets in 2019.
Madison Keys and Elina Svitolina are all set for another intriguing encounter at the US Open after straight-set victories.
Roger Federer made a big statement to the rest of the draw with a straight-sets hammering of Britain's Dan Evans at US Open 2019.
Exploring Madison Keys' constant battle with the pressure of being tipped for success from an early age.
Elina Svitolina survived two fightbacks from Venus Williams as she beat the American 6-4 6-4 to advance to the third round of US Open 2019.
Rafael Nadal breezed into the second round of US Open 2019 with a comfortable straight-sets victory over John Millman.
Simona Halep talked about her high level of self-belief and her relief at ending her sequence of US Open first-round losses.
Serena Williams breezed through to the second round of the 2019 US Open with a straight-sets hammering of long-time rival Maria Sharapova.
Daniil Medvedev talked about how beating Djokovic boosted his confidence and his reaction to Nishikori's words of encouragement.
Serena Williams versus Maria Sharapova is the headline clash in an intriguing 2019 US Open Women's Singles Draw.
Madison Keys capped an outstanding week by beating Svetlana Kuznetsova in straight sets to take home the Cincinnati title.
Madison Keys set up a intriguing final against Svetlana Kuznetsova with an excellent straight-sets win over Sofia Kenin in the semi-finals.
Elina Svitolina got the better of Karolina Muchova in two rollercoaster sets to progress to her first Grand Slam semi-final.
Johanna Konta earned her second top-ten win in a row by beating Petra Kvitova to advance to the Wimbledon quarter-finals.
Simona Halep continued her impressive progress at Wimbledon 2019 with a comfortable straight-sets win over teen sensation Cori Gauff.