Adelaide International Tennis: Iga Swiatek went into the tournament as world number 18 but will now rise to a career-high 15 as a result of the win, her first hard-court title.
Elina Svitolina became the latest seed in the women's draw to make an exit after being well beaten by unseeded Garbine Muguruza in the third round.
Naomi Osaka bumped into Beyonce and her husband Jay-Z while still "depressed" after losing in the fourth round at the US Open last year.
Ashleigh Barty and Belinda Bencic both advanced to the semi-finals after contrasting victories at the WTA Finals in China.
US Open: Serena Williams, who is seeking a 24th Grand Slam singles title to match Margaret Court's all-time record, brushed aside fifth seed Elina Svitolina 6-3, 6-1.
Bianca Andreescu defeated Belgium's Elise Mertens to set up a battle with Belinda Bencic for a spot in the US Open final.
Belinda Bencic ensured a return to the world rankings top-10 for the first time since June 2016 with the victory.
Naomi Osaka got tough competition from her Swiss opponent who won the first set 7-5
Simona Halep awaits either Dutch seventh seed Kiki Bertens, a finalist in Madrid last year, or 2017 US Open champion Sloane Stephens in the final.
Japan's Naomi Osaka retained the world number one spot.
Roger Federer became the first player to win three Hopman Cups, teaming with Belinda Bencic for the duo's second consecutive title.
World number two Angelique Kerber was too good for the 15th-ranked Barty in the opening match, winning 6-4, 6-4.
Serena Williams thumped dangerous Swiss teen Belinda Bencic 6-4, 6-3 to enter the second round of the Australian Open.
David Ferrer, the 13th seed,
Venus Williams defeated Maria Sakkari 7-5, 4-6, 6-3
Jelena Jankovic came from a set down to beat Belinda Bencic 4-6, 7-5, 6-4 in the Dubai Open first round.
Martina Hingis and her partner Belinda Bencic needed just over an hour to seal their 6-3, 6-2 win over Germany's Andrea Petkovic and Anna-Lena Groenefeld.
Roger Federer is also set to play men's doubles with Stan Wawrinka in 2016 Rio Olympics while Martina Hingis will play women's doubles with Belinda Bencic.
