Federer defeated Frenchman Adrian Mannarino 6-0, 7-5, 6-4 to reach his 16th Wimbledon quarter-final.
Beaten by Serena in the 2016 final, Kerber takes on Russian 14th seed Daria Kasatkina, a 6-7 (6/8), 6-3, 6-2 victor against Belgian world number 47 Alison Van Uytvanck. "It was a good win but it was tougher than the scoreline to be honest".
Williams, who is seeking an eighth Wimbledon title, was even more efficient, needing 62 minutes to dispatch the 120th-ranked Evgeniya Rodina, 6-2, 6-2.
Bertens, who was contemplating retirement previous year after losing her enthusiasm for the sport, is the first Dutch woman to reach the Wimbledon quarterfinals since Michaella Krajicek in 2007.
Meanwhile the last top 10 seed in the ladies' draw, Karolina Pliskova, has also been sent packing.
But the Argentine broke back immediately with a volley and then saved another break point at 5-5 with an ace. She beat the ninth-seeded Williams in the third round after coming from a break down in the third set.
Shapovalov's Wimbledon ended in the second round.
Isner rode his big serve to advance over the Greek teenager 6-4, 7-6 (8), 7-6 (4). "I can't come here and say, of course I want to play against the best players because that is not what anyone wants to do".
Leading, 5-4, and two points away from taking the first set at 0-30 on Hsieh's serve, Cibulkova struck a backhand onto the baseline that was called out.
Bizarrely, organisers chose to put a mixed doubles match on Centre Court, which was concluded under the roof after sunset.
"I'm more concerned the World Cup final will have issues because the Wimbledon final is going on".
Giorgi, 26, had failed to get past the third round of a major since the 2013 U.S. Open.
Rafael Nadal is in the quarterfinals at Wimbledon for the first time since 2011.
The top-ranked Nadal bludgeoned 37 winners to take down unseeded Czech Jiri Vesely 6-3, 6-3, 6-4 and reach the last eight for the first time in seven years.
Later on Monday, Rafael Nadal also extended his streak of not dropping a set in Wimbledon.
He managed three more holds before a sloppy game handed Federer the break to take the second.
The legendary Swiss, eyeing a ninth title at SW19, will now await the victor of either eighth seed Kevin Anderson and Gael Monfils. The only different thing is that it's Federer in front of me, and he's a really good opponent. He's notoriously had trouble on grass in recent years, but he long ago proved he can play on the turf, reaching five straight finals and winning two from 2006-2011.