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.
Roberto Bautista Agut will face Stefanos Tsitsipas for a place in the semifinals.
Marin Cilic took to Facebook to apologise to his fans and organisers of the tournament.
Croatia dethroned defending champions France and secured their second Davis Cup, 13 years after their first.
Novak Djokovic has enjoyed a remarkable renaissance in the second half of the season after an elbow surgery.
Alexander Zverev is the youngest semi-finalist at the ATP Finals since Juan Martin del Potro in 2009.
Roger Federer and Novak Djokovic, along with six fellow tennis stars travelled to Westminster by the London Underground.
Marin Cilic crashed out of the Japan Open in a shock 3-6, 6-4, 7-6 defeat to Germany's Jan-Lennard Struff in the first round.
Kei Nishikori and Naomi Osaka made history at the US Open on Wednesday when they became the first Japanese man and woman to reach the semi-finals at the same Grand Slam.
Novak Djokovic is aiming to lift the trophy at the only one of the Masters 1000 series events that he has never won.
World number one Nadal defeated Mikhail Kukushkin of Kazakhstan 6-4, 6-3, 6-4 and will next face Australian teenager Alex de Minaur.
Marin Cilic suffered a shock Wimbledon second round exit as last year's runner-up blew a two-set lead in his 3-6, 1-6, 6-4, 7-6 (7/3), 7-5 loss to Argentina's Guido Pella on Thursday.
Marin Cilic was crowned Queen's Club champion for the second time as the Croatian stunned Novak Djokovic with a dramatic fightback.
Novak Djokovic reached his first title match for a year with a straight sets win over Jeremy Chardy at Queen's Club.
Highly-rated Canadian teenager Denis Shapovalov was knocked out by Germany's Maximilian Marterer 5-7, 7-6 (7/4), 7-5, 6-4.
The 2014 US Open champion Marin Cilic needed just an hour and five minutes to clinch his third win over the 11th-ranked Spaniard.
Juan Martin del Potro sent his devoted fans home happy Tuesday by powering into the ATP Miami Open quarter-finals with a 6-4, 6-2 triumph over Serbian Filip Krajinovic.
Marin Cilic qualified for the quarterfinals in Miami with his 7-5 and 7-6 (4) victory over Canada's Vasek Pospisil.