Roger Federer became the oldest number one singles player in tennis history after beating Robin Haase in the ABN AMRO World Tennis Tournament quarter-finals in Rotterdam on Friday.
The 36-year-old Swiss, who won his 20th grand slam last month by claiming a sixth Australian Open title, replaced Rafael Nadal at the top of the ATP rankings with a 4-6 6-1 6-1 victory over Dutchman Haase.
Federer has surpassed Andre Agassi as the oldest player to occupy the summit of the men's game - the American was 33 when he was last on top in September 2003.
He will now meet Andreas Seppi in the semi-final after the Italian saw off Daniil Medvedev 7-6 (7/4) 4-6 6-3.
Second seed Grigor Dimitrov is also through to the last four after a comfortable win over Andrey Rublev.
The Bulgarian won 6-3 6-4 thanks to a break in each set and he now faces fourth seed David Goffin.
Belgian Goffin advanced without even having to step on court as his last-eight opponent Tomas Berdych withdrew through to illness.
In Buenos Aires, Dominic Thiem set up a a semi-final clash with Gael Monfils at the Argentina Open.
The world number six triumphed 7-6 (9/7) 6-4 over home favourite Guido Pella, while Monfils saved three of five break points as he defeated another Argentinian, Leonardo Mayer, 6-4 3-6 6-3.
Meanwhile, Slovenia's Aljaz Bedene upset fifth seed Diego Schwartzman in straight sets, winning 6-4 6-4 as he bids to advance to his third ATP World Tour final.
He will face Federico Delbonis in the semi-final, who battled past 34-year-old Guillermo Garcia-Lopez 6-3 7-5 after one hour and 25 minutes on court.
Kei Nishikori rallied from behind to beat Moldovan Radu Albot 4-6 6-3 6-1 and progress to the semi-final at the New York Open.
The world number 27 will meet top seed Kevin Anderson in the last four, after the South African eliminated American Frances Tiafoe 6-3 5-7 6-4 in two hours and four minutes.
Second seed Sam Querrey lost just six points on serve as he defeated 38-year-old Ivo Karlovic 7-6 (7/5) 7-6(7/4).
His semi-final will feature fourth seed Adrian Mannarino, following his win over Adrian Menendez-Maceiras 7-5 2-6 6-3.