His play already has fans and commentators dreaming of another final between Nadal and Roger Federer - on the 10th anniversary of their five-set classic that the Spaniard won.
His opponent on Wednesday is eighth-seeded Anderson, the first South African since Wayne Ferreira in 1994 to get to the last eight.
"You always tend to play better against better players and I am happy to be back in the second week of Wimbledon".
Williams dropped her first set at this tournament as the 52nd-ranked Giorgi produced an impressive display of power and accuracy in the opener.
Williams will play Camila Giorgi for a last-four berth after the Italian progressed to her maiden grand slam quarter-final with a 6-3 6-4 defeat of Ekaterina Makarova. "I will try to hold my service games most of the time".
Bertens and Pliskova had reached the fourth round at Wimbledon for the first time.
Anderson added that Federer, who won his first Wimbledon title in 2003, is the flawless role model for the sport - and for those players in the chasing pack.
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It's the first time Isner, 33, has reached the Wimbledon quarterfinals, and it is just his second quarterfinal at a major.
Djokovic was involved in a heated match with current British No. 1 Kyle Edmund on Saturday, which resulted in him blowing kisses at the Centre Court crowd amid jeers and boos, but Murray believes that was a positive reaction from the three-time Wimbledon victor.
The 12th seed faces Kei Nishikori on Wednesday ahead of a possible semi-final with Nadal and Murray on Tuesday talked up the possibility of Djokovic pulling off what would be a significant upset by taking the crown.
And this year is turning out to be a ideal environment for Rafa to reestablish his winning ways at the All-England Club. "It never happened to me in my career", Cibulkova fumed.
The fifth-seeded del Potro failed to convert four match points when serving at 5-4 in the fourth set, but maintained his composure to close out the contest with his first opportunity in the tiebreaker that followed.
"It's definitely helped a certain style of player, maybe the big servers", said 20-time major victor Federer. Like Federer, Nadal, and every other player in the quarters, he is also three wins away from Wimbledon glory, and is focused on writing his own story as opposed to being part of another, supposedly inevitable tale.
On Wednesday on Centre Court, he will start as underdog against Nadal, the 17-time major victor who is in the quarter-finals at Wimbledon for the first time since 2011 when he went on to finish runner-up.
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