Stephens defeated Keys 6-3, 6-0 for first ever Grand Slam.
Nadal won in four sets and will play Kevin Anderson in the final.
Murray is unlikely to play again in 2017 after announcing an extended break due to a hip injury.
17-year-old Sharapova defeated Williams in the 2004 Wimbledon final.
Nadal takes on Juan Martin del Potro in the semi-finals of the 2017 US Open.
Federer admits that his game, along with his mind and body, were not good enough to win the US Open this time around.
Spaniard insists his "best level" should be good enough to reach his fourth final in New York.
Nadal will take on Federer's conqueror Del Potro in the semi-final at the 2017 US Open.
Del Potro defeated Roger Federer to set up a semi-final clash with Nadal.
Del Potro defeated Federer in four sets to reach the US Open semi-final.
British number one withdraws from upcoming events in Beijing and Shanghai.
Thiem exited the US Open after surrendering a two-set lead to Juan Martín del Potro.
Del Potro ended Federer's five-year winning streak at the US Open with 2009 final defeat.
Spaniard to face 19-year-old Andrey Rublev for place in the last four at Flushing Meadows.
Nadal and Federer are on course to face each other for the first time in Flushing Meadows.
Federer and Nadal are through to the quarter-final after their straight-set wins.
Shapovalov has jumped from 143 to 69 in the world rankings.
Federer and Nadal could face each other in the semi-finals of the 2017 US Open.
Sharapova and Muguruza were both knocked out in the fourth round.
Zverev believes playing good tennis for so many years has led to recent withdrawals.
The 36-year-old defeated Lopez 6-3, 6-3, 7-5 in a one-sided match.
Shapovalov defeated Jo-Wilfried Tsonga in straight sets in the second round of the 2017 US Open.
15-time Grand Slam champion faces Leonardo Mayer after lacklustre wins over Dusan Lajovic and Taro Daniel.
Nadal is currently world number one for the first time since July 2014.
The Russian sportswoman is set to release her book Unstoppable: My Story So Far which hits the stands on 12 September.
Nadal defeated Daniel in a 4-6, 6-3, 6-2, 6-2 victory.
Murray withdrew from the event right after the draw was made.
Federer defeated Frances Tiafoe in a five-set victory on Tuesday (29 August).
Federer has been beaten just thrice in 38 matches in 2017.
The former world number one defeated Halep 6-4, 4-6, 6-3.