MELBOURNE, Australia -- Sloane Stephens has heard a lot of advice from Serena Williams. Pointers on her groundstrokes, and even on her grunts.
It's been mostly gentle encouragement, occasionally spiced with headline-making comments from Williams, who has predicted the 19-year-old American will one day top the women's rankings.
As Stephens learned earlier this month, though, it's one thing to play with Williams, another to play against the 15-time Grand Slam champion.
When they meet Wednesday at the Australian Open, Williams will have the experience of 34 previous Grand Slam quarterfinals behind her. With a comeback 6-1, 3-6, 7-5 win over Bojana Jovanovski, Stephens qualified for her first quarterfinal at a major tournament.
"It will be tough, obviously. It's quarters of a Grand Slam," Stephens said. "There won't be that, like, first time, ‘Oh, my God, I'm playing Serena.' That's kind of out of the window now. So that's good."
Williams and defending champion Victoria Azarenka advanced Monday, losing just four games between them against Russian rivals. Williams beat No. 14 Maria Kirilenko 6-2, 6-0, and Azarenka defeated Elena Vesnina 6-1, 6-1.
Next up for Azarenka is a quarterfinal against Svetlana Kuznetsova, who entered the season's first major tournament ranked No. 75 but has won titles at the 2004 U.S. Open and 2009 French Open.
On the men's side, No. 2 Roger Federer and U.S. Open champion Andy Murray stayed on course for a semifinal in their half of the draw.
Federer won 6-4, 7-6 (4), 6-2 over big-serving Canadian Milos Raonic, advancing to the quarterfinals at a Grand Slam for the 35th consecutive time, while Murray took advantage of Gilles Simon's fatigue for a 6-3, 6-1, 6-3 victory.
Federer will face 2008 Australian finalist Jo-Wilfried Tsonga, who beat friend and fellow Frenchman Richard Gasquet 6-4, 3-6, 6-3, 6-2.
Murray, who ended a 76-year drought for British men in Grand Slam tournaments with a win at the U.S. Open, will next play unseeded Frenchman Jeremy Chardy.
Chardy, who hit with Williams in a training camp at Mauritius at the end of 2012, followed up his upset win over 2009 U.S. Open champion Juan Martin del Potro with a 5-7, 6-3, 6-2, 6-2 victory over No. 21 Andreas Seppi.
Top-ranked Novak Djokovic, who needed five hours to beat Stanislas Warwinka in the fourth round, is on the other side of the draw. He'll face No. 5 seed Tomas Berdych on Tuesday.
Williams played Stephens at the Brisbane International earlier this month, winning their quarterfinal 6-4, 6-3 en route to the title. That night, Stephens said, she "lost to the best player in the world."