Federer and Nadal set up their 40th career showdown by each overcoming a tough opening set in the quarterfinals Wednesday before moving on.
The No. 2-seeded Federer, with a 4-6, 6-1, 6-4, 6-4 victory over Kei Nishikori, won his 100th match win at the All England Club, becoming the first man to reach that total at any Grand Slam tournament.
Not long after that ended on Centre Court, the No. 3-seeded Nadal finished off unseeded Sam Querrey 7-5, 6-2, 6-2 at Court No. 1.
"I had a lot of defeats; I had a lot of victories," Nadal said of his rivalry with Federer. "[Our] relationship never changed. Always big respect. Good friendship, relationship. That's all. Probably will not change if I win, if I lose."
Said Federer: "Obviously, I know people always hype it up."
Well, why shouldn't they? These are, after all, two of the greatest players in history, winners of more Grand Slam titles than any other men who have played tennis. Of Federer's 20 Grand Slam titles, a record eight came at Wimbledon. Of Nadal's 18 major trophies, 12 came at the French Open, where he routed Federer in the semifinals last month.
That gave Nadal a 24-15 career edge head-to-head, including 10-3 at the Slams.
"No, no," a smiling Nadal said when asked if he was expecting new things from Federer this time around. "I just expect to play against probably the best player in the history of this surface and know that I have to play my best if I want to have chances to try to be in that final. That's all.
"I know he's playing well. He feels comfortable here. And me, too. I'm playing well, too."
This is their fourth matchup at Wimbledon -- and first that won't come in the final. Federer beat Nadal for the 2006 and 2007 titles, but Nadal won the championship 11 years ago in a 9-7 fifth set as dusk descended after a match that lasted 4 hours, 48 minutes -- a men's final record.
"Well, we have a lot of information on Rafa, and so does he about us," Federer said. "So you can either dive into tactics and all that stuff like mad for two days -- or you're just going to say: 'You know what? It's grass-court tennis and I'm going to come out there and play attacking tennis.' And if he can defend that, that's too good. And if he can't, well, then, that's good for me."
It is the 13th time that the Big Three of Federer, Nadal and Djokovic are in the semifinals at a major tournament together. On 11 of the previous occasions, one of them claimed the title.
Djokovic used a 10-game run to transform what was shaping up as an even, entertaining quarterfinal into a lopsided romp.
"I felt," Djokovic said, "like I managed to dismantle his game."
Down an early break, the defending champion grabbed control midway through the opening set and never let go, overwhelming the 21st-seeded David Goffin 6-4, 6-0, 6-2 to reach his ninth semifinal at the All England Club.
"He was everywhere," Goffin said.
Bautista Agut, a first-time Grand Slam semifinalist, is supposed to be on the island of Ibiza right now, having a bachelor party with a half-dozen pals ahead of his November wedding. Instead, he will play on after beating No. 26 Guido Pella of Argentina 7-5, 6-4, 3-6, 6-3.
"Well," the 31-year-old Bautista Agut said, "it feels better to be here in London."
He and Nadal give Spain two men's semifinalists at Wimbledon in the same year for the first time.
Nadal won in straight sets, but it wasn't always easy. He wasted three set points at 5-3 in the opener, then another before getting broken when serving for it at 5-4. And again serving for that set at 6-5, he erased a trio of break points for the 65th-ranked Querrey before holding -- and Nadal was on his way.
As Federer made his way off Centre Court after moving into the tournament's semifinals for the 13th time, a spectator reminded him of yet another milestone. He is the first player to win 100 matches at one Grand Slam tournament.
"The fan told me, 'Congratulations, Roger, on your 100th,'" Federer said. "I'm like, 'Oh, yeah, that's right.'"
Just another mark among many for the guy, who is now 100-12 here.
Djokovic is seeking his fifth Wimbledon championship and 17th Grand Slam trophy overall. He became the fourth man in the Open era to play 70 matches at Wimbledon and tied Boris Becker, Arthur Gore and Herbert Lawford for third all time with his ninth semifinal.
The eighth-seeded Nishikori jumped out to an early edge by breaking Federer in the very first game, enough to give him that set.
"The beginning," Federer said, "was brutal."
But he quickly turned things around in the second, conjuring up whatever he wanted, exactly when he wanted it.
His approach shots were beyond reproach. His volleys vibrant. His returns were timed so well, and struck so violently, that one knocked the net-rushing Nishikori's racket plum out of his hands.
And Federer's serve? Sure, he faced break points, but he never allowed Nishikori, the 2014 US Open runner-up, to convert another.
Goffin started well enough against Djokovic on an afternoon that was humid and sunny, with the temperature in the mid-70s.
Hoping to reach his first major semifinal, Goffin claimed three of the first four points that lasted at least 10 strokes. He won the pair's most recent encounter, on clay in 2017, and this looked a bit like it was being contested on that slower surface, too.
Goffin was able to hang in there at the baseline and his on-the-run passing shots were dialed in. He nosed ahead after 33 minutes by breaking to go up 4-3, then jogged to the sideline with a raised fist.
Until then, Goffin was playing crisply and cleanly. He hadn't faced so much as one break point against Djokovic, generally considered the top returner in the game.
"He was dictating the play from the baseline," Djokovic said afterward. "Most of the rallies went his way."
But that's when everything changed.
Djokovic did to Goffin exactly what he does to so many men on so many surfaces and at so many tournaments: He takes their best shot, deals with it and then wears them down.
"I sincerely hope," Djokovic said, "that my opponent feels like he's got to work twice as [hard as] against any other opponent to win a point."
The Associated Press and ESPN Stats & Information contributed to this report.