Williams is through to the second week of a Grand Slam for the 58th time in her career after seeing off Estonian Kaia Kanepi in three sets at Flushing Meadows in New York.

The six-time US Open champion got off to a storming start but Kanepi forced a three set test after winning the second.

The match finished 6-0, 4-6, 6-3 and Williams will now play Karolína Plíšková of the Czech Republic in the quarter finals.

Plíšková beat Australia's Ashleigh Barty in straight sets to set up the rematch of the 2016 semi-finals against Williams.

"It will be a dream to play again in Arthur Ashe Stadium and to play Serena, because obviously last match we played, I won," she said.

"Since then, we didn't play. 

"A lot of things happened in between."

Defending champion Stephens is also safely through to the last eight after dismissing Belgium's Elise Mertens in straight sets, 6-3, 6-3.

Stephens has now won 11 consecutive US Open matches and produced the shot of the day, showing off her speed to retrieve a lob by Mertens and fire back a precise cross-court forehand.

The American will now play Anastasija Sevastova of Latvia in the next match, a repeat of their quarter-final head to head last year.

With the losses of Caroline Wosniacki, Simona Halep and Angelique Kerber, the women's game is guaranteed to have four different Grand Slam champions this year.

In the men's draw, Spain's Nadal was tested by another four set match, this time against Georgian Nikoloz Basilashvili.

Nadal, who won the match 6-3, 6-3, 6-7, 6-4, has now been on court for 11 hours and five minutes across four matches.

The defending champion will now play Dominic Thiem of Austria as he aims to seal the defence of his title.

If Nadal is successful it will be the first title he has defended outside of Roland Garros.

Thiem defeated South African Kevin Anderson to prevent a rematch of last year's final.

The Austrian won 7-5, 6-2, 7-6.

Juan Martin del Potro is also through to the quarter-finals after a straight sets victory over Croatia's Borna Coric.

The Argentine and 2009 US Open champion will now face fellow serving giant, John Isner, in the next round.

Isner, who returns to the US Open last eight for the first time since 2011, defeated Canada's Milos Raonic in five sets.

Raonic has now lost five of six meetings against the 33-year-old American, who won this match 3-6, 6-3, 6-4, 3-6, 6-2.

"I've definitely struggled with him, specifically," said Raonic.

Day eight of the event takes place tomorrow as the last quarter-final places are decided.