Coming into the tournament seeded 25, Williams has returned to form in spectacular fashion. "I could not go out, as much as I love her, I don't think I could do it every single day like my dad did". So it's really cool.
Goerges, seeded number 13, beat Donna Vekic of Croatia 6-3 6-2.
Kerber needed seven match points to close out No. 14 Daria Kasatkina of Russian Federation 6-3, 7-5 at Centre Court, while Ostapenko defeated 2014 Australian Open runner-up Dominika Cibulkova of Slovakia 7-5, 6-4 at a windy No. 1 Court.
41 - the number of Grand Slam appearances John Isner needed to reach his first semifinal. Her loss marks the first time in the Open era that any major has featured a quarterfinal round without a top-10 seed on either the men's or women's side, according to ESPN Stats & Information. "We've played so many tough matches", said Kerber, who sealed the win on her seventh match point and is the highest seeded player remaining in the draw.
The other last-eight matches have 2017 French Open champion Jelena Ostapenko take on Dominika Cibulkova in a meeting of former Wimbledon quarterfinalists, while 13th-seeded Julia Goerges and 20th-seeded Kiki Bertens have both reached this stage at the All England Club for the first time.
It did not even matter that her fellow seeds would avoid her in the draw, given their exodus but it was the unseeded Giorgi that presented her biggest challenge to date.
The two-time Grand Slam champion from Germany defeated No. 14 Daria Kasatkina 6-3, 7-5 on Centre Court to reach the semifinals at the All England Club for a third time.
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Prime Minister Theresa May also tweeted out her support to the players and said it had been a "great journey". We're gutted, we've worked so hard and the fans were unbelievable .
Serena Williams celebrates after winning her quarterfinals match at Wimbledon on July 10, 2018 in London. Kerber served for the victory at 5-4 in the second set, but got broken.
There was controversy at the end of the first set when the match referee was called over an incorrect line call, which caused a delay of around seven minutes before the point was replayed. You can't plan for them anyway because one point can change the outcome of a set.
The incident raised questions about Cibulkova's conduct but Hsieh said: "I understand". Federer secured his spot in the quarterfinals having won 32 consecutive sets at Wimbledon.
Cibulkova will face Jelena Ostapenko after the Latvian, last year's French Open victor, beat Aliaksandra Sasnovich 7-7 (7/4) 6-0. Of the five points he lost in the 16-minute opener, three were in the final game, when he faced his first break point of the tournament - and answered it with an ace.
But she failed in her bid to become the first Dutchwoman to make the Wimbledon last four since Betty Stove in 1977.
The 21-year-old Latvian revealed she has a novel way of improving her balance and composure on the tennis court - ballroom dancing.
Nine-time Wimbledon champion and BBC pundit Martina Navratilova said: "She's been healthy here, hitting the ball hard and the seas have parted for her". "In this tournament, she seems to be in the right mood".