Pablo Cuevas was the only seed to fall at the Argentina Open, beaten by Frenchman Gael Monfils.
Garbine Muguruza won her first match with Conchita Martinez back her in corner, while Petra Kvitova continued her winning streak in Qatar.
Donald Young accused Ryan Harrison of racism at the New York Open and the ATP will investigate.
Beginning the year by winning the Australian Open and returning to world number one means Caroline Wozniacki can take a relaxed approach.
Garbine Muguruza took eight match points to complete her victory over Duan Ying-Ying at the Qatar Open.
Donald Young says he was the subject of derogatory remarks made by fellow American tennis player Ryan Harrison, who has denied the claims.
Roger Federer's form late in his career is "amazing to watch", according to John McEnroe.
Ryan Harrison was the only seed to progress at the inaugural New York Open on Monday.
As three wildcards fell in the Argentina Open first round, Thomaz Bellucci and Guillermo Garcia-Lopez progressed.
Third seed Alexander Zverev moved into the second round of the Rotterdam Open on Monday, but his brother Mischa is out.
Records will be shattered on Monday when Roger Federer once again sits atop the ATP world rankings.
Caroline Wozniacki secured passage to the third round of the Qatar Open, building on her Australian Open title with a comfortable win.
Caroline Wozniacki will hold onto the number-one ranking after Simona Halep withdrew from the Qatar Open, despite reaching the semi-finals.
Julia Goerges had to pull out of her quarter-final at the Qatar Open, allowing Petra Kvitova a walkover route to the semis.
Caroline Garcia made an impressive start to her Qatar Open quarter-final with Garbine Muguruza, but it was the Spaniard who prevailed.
It has been over five years since it last happened, but Roger Federer is back at world number one after reaching the Rotterdam Open semis.
American teenager CiCi Bellis paid the price for a poor first set in a quarter-final defeat to second seed Simona Halep at the Qatar Open.
Roger Federer described winning his 97th career title and returning to the top of the rankings as "very special" after his win in Rotterdam.
A second straight title for Petra Kvitova came courtesy of her 13th successive win in a classic with Garbine Muguruza in Doha.
It took less than an hour for Roger Federer to see off Grigor Dimitrov in the Rotterdam Open final on Sunday.